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If the radius of a right circular cylinder is increased by 20%, then t

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If the radius of a right circular cylinder is increased by 20%, then t  [#permalink]

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New post 27 Oct 2018, 18:46
3
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (01:12) correct 42% (01:50) wrong based on 53 sessions

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If the radius of a right circular cylinder is increased by 20%, then the height would need to be approximately decreased by what percent to keep the volume unchanged?

a.15
b. 20
c. 25
d.30
e.40
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Posts: 7212
Re: If the radius of a right circular cylinder is increased by 20%, then t  [#permalink]

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New post 27 Oct 2018, 19:35
Turkish wrote:
If the radius of a right circular cylinder is increased by 20%, then the height would need to be approximately decreased by what percent to keep the volume unchanged?

a.15
b. 20
c. 25
d.30
e.40


Volume= \(πr^2h\)
So \(π(1.2r)^2h_2=π*1. 44*r^2h_2=πr^2*(1.44h_2)\)
Buy \(πr^2(1.44h_2)=πr^2h......1.44h_2=h.......h_2=\frac{h}{1.44}\)..
So decrease is \(h-\frac{h}{1.44}=\frac{0.44h}{1.44}\)
Now 0.44/1.44=11/32<1/3 that is slightly less than 33.33%
D fits in
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Re: If the radius of a right circular cylinder is increased by 20%, then t  [#permalink]

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New post 28 Oct 2018, 05:38
Let Radius be r and height be h
Volume = pir r^2 h

Increased radius = r+(r/5)= 6r/5
Volume increased by (36/25)

To make the volume be the same , height should decrease by (11/36)
i.e h-(11/36)h= (25/36)h

To get percent decrease, (11/36)*100=~ 30 %
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Re: If the radius of a right circular cylinder is increased by 20%, then t  [#permalink]

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New post 28 Oct 2018, 06:28
starting radius be 100 units
new r = 100*1.2*1.2 = 144
% decrease in height = 44 / 144 = 30% approx
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Re: If the radius of a right circular cylinder is increased by 20%, then t  [#permalink]

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New post 28 Oct 2018, 13:47

Solution



Given:
    • Radius of a right circular cylinder is increased by 20%.

To find:
    • Percent decrease in height so that volume remains unchanged.

Approach and Working

    • Volume of a right circular cylinder= π*\(R^2\)*h
If R is increased by 20% then new R will be 1.2 R.
    • New height= H
    • New volume of cylinder= π*\((1.2R)^2\)*H

However, new volume= Old volume
    • π*\((1.2R)^2\)*H = π*\(R^2\)*h
    • 1.44 \(R^2\) *H= \(R^2\) *h
    • 1.44 H=h
    • H= h/1.44 = 0.6944h = 0.7h
Therefore, percentage reduction in height= 30%

Correct answer: Option D
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Re: If the radius of a right circular cylinder is increased by 20%, then t &nbs [#permalink] 28 Oct 2018, 13:47
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