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sqdancefan

The volume of the original cylinder is

... V = π·r²·h

For r=1 and h=1, this is

... V = π·1²·1 = π

For the new cylinder, the volume is 1.089 times that amount.

... V = 1.089π = π·1.1²·(1-k)

... 1.089/1.21 = 1-k

... k = 1 - 1.089/1.21 = 1 - 0.9 = 0.1 = 10%

The appropriate choice is (B) 10.

LammettHash

Let [tex]V,r,h[/tex] be the volume, radius, and height of the original cylinder, respectively.

The new cylinder has a volume 8.9% greater than its original volume, which means the new volume is [tex]V+0.089V=1.089V[/tex]. The radius was increased by 10%, so the new radius is [tex]r+0.1r=1.1r[/tex]. The height was decreased by [tex]k\%[/tex], which means the new height is [tex]h-0.01kh=(1-0.01k)h[/tex].

Recall that the volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is

[tex]V=\pi r^2h[/tex]

So for the new cylinder, the volume equation is

[tex]1.089V=\pi(1.1r)^2((1-0.01k)h)[/tex]

[tex]1.089V=1.21(1-0.01k)(\pi r^2h)[/tex]

Now [tex]V=\pi r^2h[/tex], so we can cancel those factors and solve for [tex]k[/tex]:

[tex]1.089=1.21(1-0.01k)\implies0.9=1-0.01k\implies0.01k=0.1\implies k=10[/tex]

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