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# Problem on Cylinder | AMC-10A, 2004 | Problem 11

Try this beautiful problem from AMC 10A, 2004 based on Mensuration: Cylinder. You may use sequential hints to solve the problem.

Try this beautiful problem from AMC 10A, 2004 based on Mensuration: Cylinder

## Problem on Cylinder – AMC-10A, 2004- Problem 11

A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by $25\%$ without altering the volume, by what percent must the height be decreased?

• $16$
• $18$
• $20$
• $36$
• $25$

### Key Concepts

Mensuration

Cylinder

Percentage

Answer: $36$

AMC-10A (2004) Problem 11

Pre College Mathematics

## Try with Hints

Let the radius of the jar be $x$ and height be $h$.then the volume (V) of the jar be$V$= $\pi (x)^2 h$. Diameter of the jar increase $25$% Therefore new radius will be $x +\frac{x}{4}=\frac{5x}{4}$ .Now the given condition is “after increase the volume remain unchange”.Let new height will be $h_1$.Can you find out the new height….?

can you finish the problem……..

Let new height will be $H$.Therefore the volume will be $\pi (\frac{5x}{4})^2 H$.Since Volume remain unchange……

$\pi (x)^2 h$=$\pi (\frac{5x}{4})^2 H$ $\Rightarrow H=\frac{16h}{25}$.

height decrease =$h-\frac{16h}{25}=\frac{9h}{25}$.can you find out the decrease percentage?

can you finish the problem……..

Decrease Percentage=$\frac {\frac {9h}{25}}{h} \times 100=36$%