Try this beautiful problem from Mensuration: Problem based on Cylinder from AMC 10A, 2015.
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?
Mensuration
Cylinder
Answer: (D) The first height is $21 \%$ more than the second.
AMC-10A (2015) Problem 9
Pre College Mathematics
Let the radius of the first cylinder be $r_{1}$ and the radius of the second cylinder be $r_{2}$. Also, let the height of the first cylinder be $h_{1}$ and the height of the second cylinder be $h_{2}$.
Can you now finish the problem ..........
According to the problem,
$r_{2}=\frac{11 r_{1}}{10}$
$\pi r_{1}^{2} h_{1}=\pi r_{2}^{2} h_{2}$
can you finish the problem........
$r_{1}^{2} h_{1}=\frac{121 r_{1}^{2}}{100} h_{2} \Rightarrow h_{1}=\frac{121 h_{2}}{100}$
Therefore the Possible answer will be (D) The first height is $21 \%$ more than the second.
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