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AMC 10 Geometry Math Olympiad USA Math Olympiad

Problem based on Cylinder | AMC 10A, 2015 | Question 9

Try this beautiful problem from Mensuration: Problem based on Cylinder from AMC 10A, 2015. You may use sequential hints to solve the problem.

Try this beautiful problem from Mensuration: Problem based on Cylinder from AMC 10A, 2015.

Cylinder – AMC-10A, 2015- Problem 9


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?

  • (A) The second height is $10 \%$ less than the first.
  • (B) The first height is $10 \%$ more than the second.
  • (C) The second height is $21 \%$ less than the first.
  • (D) The first height is $21 \%$ more than the second.
  • (E) The second height is $80 \%$ of the first.

Key Concepts


Mensuration

Cylinder

Check the Answer


Answer: (D) The first height is $21 \%$ more than the second.

AMC-10A (2015) Problem 9

Pre College Mathematics

Try with Hints


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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