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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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New post 17 Feb 2016, 10:25
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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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New post 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.
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A glass is shaped like a right circular cylinder with a half sphere at [#permalink]

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New post 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. :)
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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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New post 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?

Thanks in advance!
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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