Last visit was: 22 Apr 2026, 22:59 It is currently 22 Apr 2026, 22:59
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
605-655 (Medium)|   Geometry|      
User avatar
yvonne0923
User avatar
Joined: 10 Apr 2011
Last visit: 04 May 2012
Posts: 30
Own Kudos:
340
 [8]
Given Kudos: 7
Posts: 30
Kudos: 340
 [8]
A glass is shaped like a right circular cylinder with a half sphere at 13 Apr 2011, 11:16
3
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

67% (02:10) correct 33% (02:33) wrong based on 246 sessions

History

Date
Time
Result
Not Attempted Yet

A glass is shaped like a right circular cylinder with a half sphere at the bottom. The glass is 7cm deep and has a diameter of 6cm, measured on the inside. If the glass is filled to the rim with apple cider, how much cider is in the glass? The formula for the volume a sphere is \(\frac{4}{3}*\pi*r^3\).

A. 18\(\pi\)
B. 36\(\pi\)
C. 54\(\pi\)
D. 81\(\pi\)
E. 108\(\pi\)


Show Spoiler
I'm confusing about the part "If the glass is filled to the rim with apple cider..." , how do we understand this problem?
Attachment:
cup.png
cup.png [ 1.2 KiB | Viewed 7136 times ]
ShowHide Answer
Official Answer
C
User avatar
fluke
User avatar
Retired Moderator
Joined: 20 Dec 2010
Last visit: 24 Oct 2013
Posts: 1,095
Own Kudos:
5,167
 [3]
Given Kudos: 376
Posts: 1,095
Kudos: 5,167
 [3]
A glass is shaped like a right circular cylinder with a half sphere at 13 Apr 2011, 12:35
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
yvonne0923
A glass is shaped like a right circular cylinder with a half sphere at the bottom. The glass is 7cm deep and has a diameter of 6cm, measured on the inside. If the glass is filled to the rim with apple cider, how much cider is in the glass? The formula for the volume a sphere is \(3/4*Pi*r^3\).

A. 18Pi
B. 36Pi
C. 54Pi
D. 81Pi
E. 108Pi

I'm confusing about the part "If the glass is filled to the rim with apple cider..." , how do we understand this problem?
Show more

I don't understand the meaning of this expression. Assuming it's trying to say "filled up to the brim" (fully filled).

And the volume of the sphere is:
\(\frac{4}{3}*\pi*r^3\)

The glass looks something like the one in the attached figure.

Attachment:
glass_with_cider.PNG
glass_with_cider.PNG [ 9.17 KiB | Viewed 20205 times ]

All we need to do is find the volume of the glass, which is volume of the hemispherical base+volume of the cylindrical top.

Volume of hemisphere = 1/2*(Volume of sphere) \(= \frac{1}{2}*\frac{4}{3}*\pi*r^3\), where r=radius of hemisphere

Volume of cylinder \(= \pi*r^2*h\), where r=radius of cylinder & h=height of cylinder

From the figure, we can see that Radius of cylinder=Radius of hemisphere
Also, the total depth of the glass= Radius of hemisphere+height of cylinder

glass has a diameter of 6cm
\(r=3 cm\)

glass is 7cm deep
\(r+h=7\)
\(3+h=7\)
\(h=4cm\)

Total Volume of the glass= Volume of hemisphere+Volume of cylinder

\(V=\frac{1}{2}*\frac{4}{3}*\pi*r^3+\pi*r^2*h\)
\(V=\frac{2}{3}*\pi*3^3+\pi*3^2*4\)
\(V=18\pi+36\pi=54\pi\)

Ans: "C"
User avatar
yvonne0923
User avatar
Joined: 10 Apr 2011
Last visit: 04 May 2012
Posts: 30
Own Kudos:
340
Given Kudos: 7
Posts: 30
Kudos: 340
A glass is shaped like a right circular cylinder with a half sphere at 13 Apr 2011, 15:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fluke
yvonne0923
A glass is shaped like a right circular cylinder with a half sphere at the bottom. The glass is 7cm deep and has a diameter of 6cm, measured on the inside. If the glass is filled to the rim with apple cider, how much cider is in the glass? The formula for the volume a sphere is \(3/4*Pi*r^3\).

A. 18Pi
B. 36Pi
C. 54Pi
D. 81Pi
E. 108Pi

I'm confusing about the part "If the glass is filled to the rim with apple cider..." , how do we understand this problem?

I don't understand the meaning of this expression. Assuming it's trying to say "filled up to the brim" (fully filled).

And the volume of the sphere is:
\(\frac{4}{3}*\pi*r^3\)

The glass looks something like the one in the attached figure.

Attachment:
The attachment glass_with_cider.PNG is no longer available

All we need to do is find the volume of the glass, which is volume of the hemispherical base+volume of the cylindrical top.

Volume of hemisphere = 1/2*(Volume of sphere) \(= \frac{1}{2}*\frac{4}{3}*\pi*r^3\), where r=radius of hemisphere

Volume of cylinder \(= \pi*r^2*h\), where r=radius of cylinder & h=height of cylinder

From the figure, we can see that Radius of cylinder=Radius of hemisphere
Also, the total depth of the glass= Radius of hemisphere+height of cylinder

glass has a diameter of 6cm
\(r=3 cm\)

glass is 7cm deep
\(r+h=7\)
\(3+h=7\)
\(h=4cm\)

Total Volume of the glass= Volume of hemisphere+Volume of cylinder

\(V=\frac{1}{2}*\frac{4}{3}*\pi*r^3+\pi*r^2*h\)
\(V=\frac{2}{3}*\pi*3^3+\pi*3^2*4\)
\(V=18\pi+36\pi=54\pi\)

Ans: "C"
Show more




I understand how to solve the problem if there is no image attached, but the image shown on the book is like a shape of glass wine below.

Attachment:
Glass_Cider.jpg
Glass_Cider.jpg [ 1.87 KiB | Viewed 19865 times ]

So if in this case, I believe that the cider is impossible to reach the holder of the glass, and I supposed to substract the height of the holder from the total height of glass of 7cm. However, how can we know the height of the holder? Also, in this case, the information of sphere volume is not really necessary here according to this image.
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 21 Apr 2026
Posts: 16,439
Own Kudos:
79,389
Given Kudos: 484
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,439
Kudos: 79,389
A glass is shaped like a right circular cylinder with a half sphere at 13 Apr 2011, 19:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
yvonne0923



I understand how to solve the problem if there is no image attached, but the image shown on the book is like a shape of glass wine below.

Attachment:
Glass_Cider.jpg

So if in this case, I believe that the cider is impossible to reach the holder of the glass, and I supposed to substract the height of the holder from the total height of glass of 7cm. However, how can we know the height of the holder? Also, in this case, the information of sphere volume is not really necessary here according to this image.
Show more

Actually, the image has been given to help you understand the question better, not confuse you. The solution is as given by fluke. Look at the figure drawn by fluke. It is the top part of the glass and that is what matters. The entire information given is for the top part only. The stem of the glass is there to just hold it and doesn't account for anything (It has been drawn so that people don't worry about how the glass will 'stand' with a round bottom).

Read the question again. Let me quote:
'The glass is 7cm deep and has a diameter of 6cm, measured on the inside. If the glass is filled to the rim with apple cider, how much cider is in the glass?'

The glass i.e. the part that will hold the liquid, is 7 cm deep so from top of cylinder to lowest point of hemisphere i.e. just the part shown by fluke is 7 cm.
The rim is the outer edge or the brink of a circular object. When we say it is filled to the rim, it means it is filled to the top i.e. the part shown by fluke in the diagram is completely filled. Just think of an actual wine glass filled to the top. Now focus on the part that holds the wine - that is the part whose dimensions are given. Forget the stem and the base. They are drawn just to satisfy you that we are talking about an actual glass.
User avatar
subhashghosh
User avatar
Retired Moderator
Joined: 16 Nov 2010
Last visit: 25 Jun 2024
Posts: 894
Own Kudos:
1,302
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
Products:
My Reviews
Posts: 894
Kudos: 1,302
A glass is shaped like a right circular cylinder with a half sphere at 13 Apr 2011, 19:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total Vol of wine = Vol of wine in Cylinder part + Vol of wine in Hemishphere

= pi*3^2* (7-3) + 2/3 * pi * 3^3

= 36pi + 18pi

= 54pi

Answer - C
User avatar
Warlock007
User avatar
Joined: 08 Jan 2011
Last visit: 25 May 2012
Posts: 149
Own Kudos:
226
Given Kudos: 46
Status:==GMAT Ninja==
Schools:ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Posts: 149
Kudos: 226
A glass is shaped like a right circular cylinder with a half sphere at 14 Apr 2011, 10:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fluke
yvonne0923
A glass is shaped like a right circular cylinder with a half sphere at the bottom. The glass is 7cm deep and has a diameter of 6cm, measured on the inside. If the glass is filled to the rim with apple cider, how much cider is in the glass? The formula for the volume a sphere is \(3/4*Pi*r^3\).

A. 18Pi
B. 36Pi
C. 54Pi
D. 81Pi
E. 108Pi

I'm confusing about the part "If the glass is filled to the rim with apple cider..." , how do we understand this problem?

I don't understand the meaning of this expression. Assuming it's trying to say "filled up to the brim" (fully filled).

And the volume of the sphere is:
\(\frac{4}{3}*\pi*r^3\)

The glass looks something like the one in the attached figure.

Attachment:
glass_with_cider.PNG

All we need to do is find the volume of the glass, which is volume of the hemispherical base+volume of the cylindrical top.

Volume of hemisphere = 1/2*(Volume of sphere) \(= \frac{1}{2}*\frac{4}{3}*\pi*r^3\), where r=radius of hemisphere

Volume of cylinder \(= \pi*r^2*h\), where r=radius of cylinder & h=height of cylinder

From the figure, we can see that Radius of cylinder=Radius of hemisphere
Also, the total depth of the glass= Radius of hemisphere+height of cylinder

glass has a diameter of 6cm
\(r=3 cm\)

glass is 7cm deep
\(r+h=7\)
\(3+h=7\)
\(h=4cm\)

Total Volume of the glass= Volume of hemisphere+Volume of cylinder

\(V=\frac{1}{2}*\frac{4}{3}*\pi*r^3+\pi*r^2*h\)
\(V=\frac{2}{3}*\pi*3^3+\pi*3^2*4\)
\(V=18\pi+36\pi=54\pi\)

Ans: "C"
Show more

Dear Fluke
as the figure was not attached how can you say that the sphere is not placed upside down
i arrived at 45Pi as i was deducting the quantity (as i thought it to be upside down)
I think it was only given options from which i could thought of adding instead of deducting the volume of sphere from the total volume of cylinder :(

please advice
User avatar
Warlock007
User avatar
Joined: 08 Jan 2011
Last visit: 25 May 2012
Posts: 149
Own Kudos:
226
Given Kudos: 46
Status:==GMAT Ninja==
Schools:ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Posts: 149
Kudos: 226
A glass is shaped like a right circular cylinder with a half sphere at 14 Apr 2011, 12:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fluke
Warlock007

Dear Fluke
as the figure was not attached how can you say that the sphere is not placed upside down
Intuition and good luck!!! :) I see that you made a genuine point here. I should have been more cautious.

i arrived at 45Pi as i was deducting the quantity (as i thought it to be upside down)
How did you arrive at \(45\pi\)? Even if the hemisphere is upside down at the bottom, the result should be \(72\pi\). Please explain. On a second thought, now that we know the hemisphere is not upside down, do we really need to do this? Up to you.

I think it was only given options from which i could thought of adding instead of deducting the volume of sphere from the total volume of cylinder :(

please advice
Show more


I have taken the hemisphere volume to be \(18\pi\) only but in case of cylinder i have taken h=7
I dont know how come you deducted the radius from the given depth 7 cm

in my approach total volume is = \(63\pi\) + \(18\pi\) =\(81\pi\)
in your approach total volume is = \(63\pi\) - \(18\pi\) =\(45\pi\)

and sorry my pick was D \(81\pi\)

please correct my approach
User avatar
fluke
User avatar
Retired Moderator
Joined: 20 Dec 2010
Last visit: 24 Oct 2013
Posts: 1,095
Own Kudos:
5,167
 [2]
Given Kudos: 376
Posts: 1,095
Kudos: 5,167
 [2]
A glass is shaped like a right circular cylinder with a half sphere at 14 Apr 2011, 12:35
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Warlock007
fluke
Warlock007

Dear Fluke
as the figure was not attached how can you say that the sphere is not placed upside down
Intuition and good luck!!! :) I see that you made a genuine point here. I should have been more cautious.

i arrived at 45Pi as i was deducting the quantity (as i thought it to be upside down)
How did you arrive at \(45\pi\)? Even if the hemisphere is upside down at the bottom, the result should be \(72\pi\). Please explain. On a second thought, now that we know the hemisphere is not upside down, do we really need to do this? Up to you.

I think it was only given options from which i could thought of adding instead of deducting the volume of sphere from the total volume of cylinder :(

please advice


I have taken the hemisphere volume to be \(18\pi\) only but in case of cylinder i have taken h=7
I dont know how come you deducted the radius from the given depth 7 cm

Depth of the glass = 7cm
If we go by the original question and original figure of the question,
7cm=Radius of hemisphere+height of cylinder
And it is given that Radius of hemisphere=3cm
7cm=3cm+height of cylinder
height of cylinder=7cm-3cm=4cm

Please see the attached image:
Red line+Green line=Depth of the glass=7cm
Red line=Radius of hemisphere= 3cm
Green line=Height of cylinder= 4cm

So, Volume of cylinder= \(\pi*r^2*h=\pi*3^2*4=36\pi\)

Attachment:
glass_with_cider.PNG
glass_with_cider.PNG [ 9.54 KiB | Viewed 19696 times ]


in my approach total volume is = \(63\pi\) + \(18\pi\) =\(81\pi\)
in your approach total volume is = \(63\pi\) - \(18\pi\) =\(45\pi\)

and sorry my pick was D \(81\pi\)

please correct my approach
Show more
User avatar
Warlock007
User avatar
Joined: 08 Jan 2011
Last visit: 25 May 2012
Posts: 149
Own Kudos:
226
Given Kudos: 46
Status:==GMAT Ninja==
Schools:ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Posts: 149
Kudos: 226
A glass is shaped like a right circular cylinder with a half sphere at 14 Apr 2011, 12:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fluke

Dear Fluke
as the figure was not attached how can you say that the sphere is not placed upside down
Intuition and good luck!!! :) I see that you made a genuine point here. I should have been more cautious.

i arrived at 45Pi as i was deducting the quantity (as i thought it to be upside down)
How did you arrive at \(45\pi\)? Even if the hemisphere is upside down at the bottom, the result should be \(72\pi\). Please explain. On a second thought, now that we know the hemisphere is not upside down, do we really need to do this? Up to you.

I think it was only given options from which i could thought of adding instead of deducting the volume of sphere from the total volume of cylinder :(

please advice
Show more
[/quote]


I have taken the hemisphere volume to be \(18\pi\) only but in case of cylinder i have taken h=7
I dont know how come you deducted the radius from the given depth 7 cm

Depth of the glass = 7cm
If we go by the original question and original figure of the question,
7cm=Radius of hemisphere+height of cylinder
And it is given that Radius of hemisphere=3cm
7cm=3cm+height of cylinder
height of cylinder=7cm-3cm=4cm

Please see the attached image:
Red line+Green line=Depth of the glass=7cm
Red line=Radius of hemisphere= 3cm
Green line=Height of cylinder= 4cm

So, Volume of cylinder= \(\pi*r^2*h=\pi*3^2*4=36\pi\)

Attachment:
glass_with_cider.PNG


in my approach total volume is = \(63\pi\) + \(18\pi\) =\(81\pi\)
in your approach total volume is = \(63\pi\) - \(18\pi\) =\(45\pi\)

and sorry my pick was D \(81\pi\)

please correct my approach[/quote][/quote]

Dear Fluke thats what confused me should i include or not the radius

actually coincidently i found \(81\pi\) in the answers too
I hope this kind of disaster would not happen in real GMAT :( :(

kudos to you :-D :-D
User avatar
ENGRTOMBA2018
User avatar
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Own Kudos:
3,889
 [2]
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
My Reviews
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
Posts: 2,319
Kudos: 3,889
 [2]
A glass is shaped like a right circular cylinder with a half sphere at Updated on: 17 Feb 2016, 10:50
Originally posted by ENGRTOMBA2018 on 17 Feb 2016, 10:38.
Last edited by ENGRTOMBA2018 on 17 Feb 2016, 10:50, edited 1 time in total.
Corrected the typo.
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Nevernevergiveup
Attachment:
cup.png
A glass is shaped like a right circular cylinder with a half sphere at the bottom. The glass is 7cm deep and has a diameter of 6cm, measured on the inside. If the glass is filled to the rim with apple cider, how much cider is in the glass? The formula for the volume a sphere is \(\frac{4}{3}*\pi*r^3\).

A. 18\(\pi\)
B. 36\(\pi\)
C. 54\(\pi\)
D. 81\(\pi\)
E. 108\(\pi\)
Show more

The glass volume is composed of 2 parts: hemispherical portion + cylindrical portion.

For the hemispherical portion, diameter = 6 cm ---> radius = r= 3 ---> volume of the hemisphere = volume of sphere /2 = \(0.5*\frac{4}{3}*\pi*r^3 = 18\pi\)

For the cylindrical part, heigh=h=7-3 = 4 and radius =3 ---> volume of the cylindrical portion \(= \pi*r^2*h = 36\pi\)

Thus the total volume =\(( 18+36 )\pi = 54\pi\)

C is thus the correct answer.

Hope this helps.
User avatar
rahul16singh28
User avatar
Joined: 31 Jul 2017
Last visit: 09 Jun 2020
Posts: 428
Own Kudos:
503
Given Kudos: 752
Location: Malaysia
Schools: INSEAD Jan '19
GPA: 3.95
WE:Consulting (Energy)
Schools: INSEAD Jan '19
Posts: 428
Kudos: 503
A glass is shaped like a right circular cylinder with a half sphere at 06 Jun 2018, 11:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
yvonne0923
A glass is shaped like a right circular cylinder with a half sphere at the bottom. The glass is 7cm deep and has a diameter of 6cm, measured on the inside. If the glass is filled to the rim with apple cider, how much cider is in the glass? The formula for the volume a sphere is \(\frac{4}{3}*\pi*r^3\).

A. 18Pi
B. 36Pi
C. 54Pi
D. 81Pi
E. 108Pi

I'm confusing about the part "If the glass is filled to the rim with apple cider..." , how do we understand this problem?
Show more

Voulume of Cidar in the Glass = Vol. of Cylinder - Vol. of Semisphere + Area of the Base of Cylinder
= \(πr^2h - 2/3πr^3 + πr^2\)
= \(54π\)
User avatar
Kimberly77
User avatar
Joined: 16 Nov 2021
Last visit: 07 Sep 2024
Posts: 421
Own Kudos:
47
Given Kudos: 5,898
Location: United Kingdom
GMAT 1: 450 Q42 V34
Products:
My Reviews
GMAT 1: 450 Q42 V34
Posts: 421
Kudos: 47
A glass is shaped like a right circular cylinder with a half sphere at 03 Jun 2022, 04:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ENGRTOMBA2018
Nevernevergiveup
Attachment:
cup.png
A glass is shaped like a right circular cylinder with a half sphere at the bottom. The glass is 7cm deep and has a diameter of 6cm, measured on the inside. If the glass is filled to the rim with apple cider, how much cider is in the glass? The formula for the volume a sphere is \(\frac{4}{3}*\pi*r^3\).

A. 18\(\pi\)
B. 36\(\pi\)
C. 54\(\pi\)
D. 81\(\pi\)
E. 108\(\pi\)

The glass volume is composed of 2 parts: hemispherical portion + cylindrical portion.

For the hemispherical portion, diameter = 6 cm ---> radius = r= 3 ---> volume of the hemisphere = volume of sphere /2 = \(0.5*\frac{4}{3}*\pi*r^3 = 18\pi\)

For the cylindrical part, heigh=h=7-3 = 4 and radius =3 ---> volume of the cylindrical portion \(= \pi*r^2*h = 36\pi\)

Thus the total volume =\(( 18+36 )\pi = 54\pi\)

C is thus the correct answer.

Hope this helps.
Show more



Greaat explanation ENGRTOMBA2018, why is volumne of sphere need to be 1/2 again when we only calculate it with r=3 ? Thanks
User avatar
ThatDudeKnows
User avatar
Joined: 11 May 2022
Last visit: 27 Jun 2024
Posts: 1,070
Own Kudos:
1,030
Given Kudos: 79
Expert
Expert reply
Posts: 1,070
Kudos: 1,030
A glass is shaped like a right circular cylinder with a half sphere at 03 Jun 2022, 06:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Kimberly77
ENGRTOMBA2018
Nevernevergiveup
Attachment:
cup.png
A glass is shaped like a right circular cylinder with a half sphere at the bottom. The glass is 7cm deep and has a diameter of 6cm, measured on the inside. If the glass is filled to the rim with apple cider, how much cider is in the glass? The formula for the volume a sphere is \(\frac{4}{3}*\pi*r^3\).

A. 18\(\pi\)
B. 36\(\pi\)
C. 54\(\pi\)
D. 81\(\pi\)
E. 108\(\pi\)

The glass volume is composed of 2 parts: hemispherical portion + cylindrical portion.

For the hemispherical portion, diameter = 6 cm ---> radius = r= 3 ---> volume of the hemisphere = volume of sphere /2 = \(0.5*\frac{4}{3}*\pi*r^3 = 18\pi\)

For the cylindrical part, heigh=h=7-3 = 4 and radius =3 ---> volume of the cylindrical portion \(= \pi*r^2*h = 36\pi\)

Thus the total volume =\(( 18+36 )\pi = 54\pi\)

C is thus the correct answer.

Hope this helps.



Greaat explanation ENGRTOMBA2018, why is volumne of sphere need to be 1/2 again when we only calculate it with r=3 ? Thanks
Show more

Hi Kimberly77,

Remember that the glass is not shaped as a cylinder sitting on top of a sphere; it a cylinder sitting on top of HALF a sphere. That's where the 1/2 comes from.

I'm surprised not to see a single answer in this thread that uses ballparking. Imagine a glass that is just a cylinder of height 7 and radius 3. Volume is (pi)(r^2)(h) = (pi)(9)(7) = 63(pi).
Do we want less than that, or more? Less. D and E are wrong.
How much less? Less than half, more than half? More. A is wrong.
51%? 75%? 99%? I don't know, let's say around 80%, maybe a little more. B is wrong.

Answer choice C.

So many geometry questions on the GMAT can be answered just by ballparking without doing the "real" math.
User avatar
Kimberly77
User avatar
Joined: 16 Nov 2021
Last visit: 07 Sep 2024
Posts: 421
Own Kudos:
47
Given Kudos: 5,898
Location: United Kingdom
GMAT 1: 450 Q42 V34
Products:
My Reviews
GMAT 1: 450 Q42 V34
Posts: 421
Kudos: 47
A glass is shaped like a right circular cylinder with a half sphere at 03 Jun 2022, 06:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Briliiant and thanks for your quick reply ThatDudeKnows, your explanation make absolute sense now.
Will tag you in future and thanks again!
Moderators:
Bunuel
Math Expert
109763 posts
Krunaal
Tuck School Moderator
853 posts