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

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A glass is shaped like a right circular cylinder with a half sphere at [#permalink]

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17 Feb 2016, 10:25
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35% (medium)

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68% (01:53) correct 32% (01:03) wrong based on 72 sessions

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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$$\pi$$

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A glass is shaped like a right circular cylinder with a half sphere at [#permalink]

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Updated on: 17 Feb 2016, 10:50
1
Nevernevergiveup wrote:
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.

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.
Retired Moderator
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A glass is shaped like a right circular cylinder with a half sphere at [#permalink]

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17 Feb 2016, 10:46
1
Engr2012 wrote:
Nevernevergiveup wrote:
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 =$$( 18+36 )\pi = 54\pi$$

D is thus the correct answer.

Hope this helps.

54$$\pi$$ and option D are different. I understand it is a typo.
_________________

The only time you can lose is when you give up. Try hard and you will suceed.
Thanks = Kudos. Kudos are appreciated

http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html
When you post a question Pls. Provide its source & TAG your questions
Avoid posting from unreliable sources.

My posts
http://gmatclub.com/forum/beauty-of-coordinate-geometry-213760.html#p1649924
http://gmatclub.com/forum/calling-all-march-april-gmat-takers-who-want-to-cross-213154.html
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http://gmatclub.com/forum/double-negatives-206717.html
http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1721773

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Re: A glass is shaped like a right circular cylinder with a half sphere at [#permalink]

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13 Mar 2017, 10:14
Engr2012 wrote:
Nevernevergiveup wrote:
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.

Sorry if I'm missing something obvious here, but how do we know to subtract 3 from the height of the glass?

Re: A glass is shaped like a right circular cylinder with a half sphere at   [#permalink] 13 Mar 2017, 10:14
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