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705-805 (Hard)|   Geometry|      
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Sasindran
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A cylinder resting on its curved surface is half full with v 28 Nov 2017, 23:53
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D
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Difficulty:

85% (hard)

Question Stats:

51% (02:18) correct 49% (02:53) wrong based on 108 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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D
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A cylinder resting on its curved surface is half full with v 29 Nov 2017, 02:55
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Sasindran
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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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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A cylinder resting on its curved surface is half full with v 29 Nov 2017, 03:42
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chetan2u
Sasindran
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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Hi chetan2u,

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

What is trap here?
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A cylinder resting on its curved surface is half full with v 29 Nov 2017, 06:52
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NandishSS
chetan2u
Sasindran
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?
Show more

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

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A cylinder resting on its curved surface is half full with v 29 Nov 2017, 07:47
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NandishSS
chetan2u
Sasindran
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?
Show more
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

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A cylinder resting on its curved surface is half full with v 29 Nov 2017, 10:30
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Sasindran
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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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
Answer is D
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A cylinder resting on its curved surface is half full with v 01 Dec 2017, 07:20
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Sasindran
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
Show more

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.

Answer: D
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A cylinder resting on its curved surface is half full with v 25 Mar 2018, 07:29
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Sasindran
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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\(\frac{22}{7} r^2\) *3 = 462 => \(r^2\) =7*7 => r=7 => d=14 Ans
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