Question

A cylinder of radius $5cm$ is inserted within a cylinder of radius $10cm$. The two cylinders have the same height of $20cm$. What is the volume of the region between the two cylinders?

• A. $1000$
• B. $500Pi$
• C. $1000Pi$
• D. $1500Pi$
• E. $2000Pi$

Answer 1

The correct option is D $1500Pi$

Solution:

Given that:

Radius of the larger cylinder $r_1=10cm$

Radius of the smaller cylinder $r_2=5cm$

Height of both cylinder $=20cm$

To find:

Volume of the region between the two cylinders$=?$

Solution:

Volume of the region between the two cylinders$=\pi r_1^{2}h-\pi r_2^{2}h$

$=\pi \times (10{)}^2\times 20-\pi \times (5{)}^2\times 20$

$=2000\pi -500\pi$

$=1500\pi$

Hence, D is the correct option.