A cylinder whose volume is 900 cubic inches is reshaped such that its

Question

A cylinder whose volume is 900 cubic inches is reshaped such that its volume remains unchanged. If its diameter is reduced by 50%, then its height must be increased by:

A. 50%
B. 100%
C. 200%
D. 300%
E. 400%

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kawal27 · Answer

and: D 300% 
--> Volume=πr2·H

--> πr2·H = 900

Plug in a nice r such as r = 10 (so that r2=100). The resulting H is = 9/π.

Now, If r is reduced by 50%, it is now 5.

Plug in the new r=5, and find the new H.

--> π·52·H = 900

--> H = 900/(25π) = 36/π

The original H was 9/π, so H is multiplied times 4. However, this only represents a 300% increase from the original height.

Archit3110 · Answer

given 
pi*r^2*h = 900
dia is 50% reduced ; r= d/4
pi*r^2/4*h=900
pi*r^2*h=3600
so change in height = 3600-900/900 ; 300%
IMO D

iamhimanee · Answer

Given- pi* r^2*h =900 
as r=d/2
so pi*(d/2)^2*h=900
pi*d^2*h=3600 ---1

the diameter is reduced to 50%
pi*(d/2)^2 *h =3600
pi*d^2 *h=14400 --2

we need to find the % increase in height :
(14400-3600/3600) *100 
on solving 300%

ScottTargetTestPrep · Answer

We can let h = the original height of the cylinder and H = the new height of the cylinder.

We can let the original diameter = 20, so we have:

900 = ?(10)^2 * h

900 = 100?h

9/? = h

If the diameter is reduced by 1/2, the radius is also reduced by 1/2, so we have:

900 = ?(5)^2 * H

900 = 25?H

36/? = H

We see that the new height is 4 times the old height; therefore, the height must be increased by 300%.

Answer: D

Paras96 · Answer

New volume = Old volume
r*r*h=0.5r*0.5r*H

H=4h

(H-h)/h= 3h/h =300%

Hence D

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A cylinder whose volume is 900 cubic inches is reshaped such that its

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