Question

Two right circular cylinders have the same volume. The radius of the second cylinder is $10\%$ more than the radius of the first. What is the relationship between the heights of the two cylinders?

The second height is $10\%$ less than the first.

The first height is $10\%$ more than the second.

The second height is $21\%$ less than the first.

The first height is $21\%$ more than the second.

The second height is $80\%$ of the first.

Solution:

Let $r_1$ and $h_1$ be the radius and height of the first cylinder and similarly define $r_2$ and $h_2$ for the second cylinder.

We know that $r_2 = \dfrac{11}{10}r_1$ and $\pi r_1^2h_1 = \pi r_2^2h_2.$

Substituting and simplifying gives us $r_1^2h_1 = \dfrac{121}{100}r_1^2h_2,$ which tells us that $h_1 = \dfrac{121}{100}h_2.$

Thus, D is the correct answer.

2015 AMC 10A Problem 9

Solution:

Problem 9 in Other Years