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Senior Manager  G
Joined: 17 Oct 2016
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A cylinder resting on its curved surface is half full with v  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 51% (02:20) correct 49% (02:49) wrong based on 65 sessions

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A cylinder resting on its curved surface is half full with volume of water as 462cu.m. What is the diameter of the cylinder if the height of the water is 3m when the cylinder is resting on its circular base?

A. 7
B. 7*(2)^0.5
C. 14*(2)^0.5
D. 14
E. 28

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Math Expert V
Joined: 02 Aug 2009
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Re: A cylinder resting on its curved surface is half full with v  [#permalink]

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Sasindran wrote:
A cylinder resting on its curved surface is half full with volume of water as 462cu.m. What is the diameter of the cylinder if the height of the water is 3m when the cylinder is resting on its circular base?

A. 7
B. 7*(2)^0.5
C. 14*(2)^0.5
D. 14
E. 28

Posted from my mobile device

Hi....

If the cylinder is HALF full while on curved surface, it will also be HALF full When on the circular base.
So the height is 3 m and volume =$$πr^2h=462......r^2=\frac{462}{π*3}=\frac{462*7}{22*3}=49.....r=7$$
So D =2*7=14

D
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Re: A cylinder resting on its curved surface is half full with v  [#permalink]

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chetan2u wrote:
Sasindran wrote:
A cylinder resting on its curved surface is half full with volume of water as 462cu.m. What is the diameter of the cylinder if the height of the water is 3m when the cylinder is resting on its circular base?

A. 7
B. 7*(2)^0.5
C. 14*(2)^0.5
D. 14
E. 28

Posted from my mobile device

Hi....

If the cylinder is HALF full while on curved surface, it will also be HALF full When on the circular base.
So the height is 3 m and volume =$$πr^2h=462......r^2=\frac{462}{π*3}=\frac{462*7}{22*3}=49.....r=7$$
So D =2*7=14

D

Hi chetan2u,

If Volume is half full then is it not $$πr^2(h/2)=462$$?

What is trap here?
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Joined: 17 Oct 2016
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Re: A cylinder resting on its curved surface is half full with v  [#permalink]

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NandishSS wrote:
chetan2u wrote:
Sasindran wrote:
A cylinder resting on its curved surface is half full with volume of water as 462cu.m. What is the diameter of the cylinder if the height of the water is 3m when the cylinder is resting on its circular base?

A. 7
B. 7*(2)^0.5
C. 14*(2)^0.5
D. 14
E. 28

Posted from my mobile device

Hi....

If the cylinder is HALF full while on curved surface, it will also be HALF full When on the circular base.
So the height is 3 m and volume =$$πr^2h=462......r^2=\frac{462}{π*3}=\frac{462*7}{22*3}=49.....r=7$$
So D =2*7=14

D

Hi chetan2u,

If Volume is half full then is it not $$πr^2(h/2)=462$$?

What is trap here?

You are missing the point that volume of the cylinder when it’s vertical = half volume of the cylinder when it’s horizontal.

Posted from my mobile device
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Re: A cylinder resting on its curved surface is half full with v  [#permalink]

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NandishSS wrote:
chetan2u wrote:
Sasindran wrote:
A cylinder resting on its curved surface is half full with volume of water as 462cu.m. What is the diameter of the cylinder if the height of the water is 3m when the cylinder is resting on its circular base?

A. 7
B. 7*(2)^0.5
C. 14*(2)^0.5
D. 14
E. 28

Posted from my mobile device

Hi....

If the cylinder is HALF full while on curved surface, it will also be HALF full When on the circular base.
So the height is 3 m and volume =$$πr^2h=462......r^2=\frac{462}{π*3}=\frac{462*7}{22*3}=49.....r=7$$
So D =2*7=14

D

Hi chetan2u,

If Volume is half full then is it not $$πr^2(h/2)=462$$?

What is trap here?

Hi NandiSS,

You are right in thinking that pi*r^2*h = 462*2.. the catch here is when it's horizontal it's height is 6.
Hope it helps

Sent from my Lenovo P1a42 using GMAT Club Forum mobile app
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Re: A cylinder resting on its curved surface is half full with v  [#permalink]

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Sasindran wrote:
A cylinder resting on its curved surface is half full with volume of water as 462cu.m. What is the diameter of the cylinder if the height of the water is 3m when the cylinder is resting on its circular base?

A. 7
B. 7*(2)^0.5
C. 14*(2)^0.5
D. 14
E. 28

Posted from my mobile device

The formula of filled cylinder is $$\pi * r^2 * H = 462 * 2$$
If H = 3 when it's half full => H = 6 when it's full
$$\frac{\pi * r^2 * 6}{2} = 462$$
$$462 = 3\pi *r^2$$

$$\frac{462}{9} = r^2$$
$$\sqrt51 = r$$
$$7 = r$$
D = 2r = 14
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Re: A cylinder resting on its curved surface is half full with v  [#permalink]

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Sasindran wrote:
A cylinder resting on its curved surface is half full with volume of water as 462cu.m. What is the diameter of the cylinder if the height of the water is 3m when the cylinder is resting on its circular base?

A. 7
B. 7*(2)^0.5
C. 14*(2)^0.5
D. 14
E. 28

Since we are given that the volume of the water is 462 m^3 and the height of the water is 3 m, if we let r = radius of the base of the cylinder, the volume of the water can be equated as follows:

462 = π x r^2 x 3

154/π = r^2

49 = r^2

r = 7

Since the radius = 7, the diameter = 14.

Note that the height of the water in the cylinder can be confusing. Yes, the actual height of the cylinder is 6 feet, but the volume of water is 462 cu. m.when the cylinder is half full. Thus, we use 3 feet for the height of the cylinder for the given volume. We could use 6 feet for the height of the cylinder, but we would have to double the given volume in order to get the correct answer.

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Joined: 24 Aug 2016
Posts: 790
GMAT 1: 540 Q49 V16 GMAT 2: 680 Q49 V33 Re: A cylinder resting on its curved surface is half full with v  [#permalink]

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Sasindran wrote:
A cylinder resting on its curved surface is half full with volume of water as 462cu.m. What is the diameter of the cylinder if the height of the water is 3m when the cylinder is resting on its circular base?

A. 7
B. 7*(2)^0.5
C. 14*(2)^0.5
D. 14
E. 28

Posted from my mobile device

$$\frac{22}{7} r^2$$ *3 = 462 => $$r^2$$ =7*7 => r=7 => d=14 Ans
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Thanks in appreciation. Re: A cylinder resting on its curved surface is half full with v   [#permalink] 25 Mar 2018, 07:29
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