A glass is shaped like a right circular cylinder with a half sphere at

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.

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

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

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

[/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= \(\pi*r^2*h=\pi*3^2*4=36\pi\)



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

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.

Voulume of Cidar in the Glass = Vol. of Cylinder - Vol. of Semisphere + Area of the Base of Cylinder
= \(πr^2h - 2/3πr^3 + πr^2\)
= \(54π\)

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

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.

Briliiant and thanks for your quick reply ThatDudeKnows, your explanation make absolute sense now.
Will tag you in future and thanks again!