Question

How do you do this problem?

Answer 1

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.

Answer 2

Let $V,r,h$ 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 $V+0.089V=1.089V$. The radius was increased by 10%, so the new radius is $r+0.1r=1.1r$. The height was decreased by $k\%$, which means the new height is $h-0.01kh=(1-0.01k)h$.

Recall that the volume of a cylinder with radius $r$ and height $h$ is

$V=\pi r^2h$

So for the new cylinder, the volume equation is

$1.089V=\pi(1.1r)^2((1-0.01k)h)$

$1.089V=1.21(1-0.01k)(\pi r^2h)$

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

$1.089=1.21(1-0.01k)\implies0.9=1-0.01k\implies0.01k=0.1\implies k=10$