Question

From a circular cylinder of diameter $10cm$ and height $12cm$, a conical cavity of the same base radius and of the same height is hollowed out. Find the volume of the remaining solid. Leave the answer in $\pi$.

• A. $210\pi$ $c{m}^3$
• B. $660\pi$ $c{m}^3$
• C. $220\pi$ $c{m}^3$
• D. $200\pi$ $c{m}^3$

Answer 1

Answer: (D)

$200\pi$ $c{m}^3$

Given the radius of base of the circular cylinder is $\left(r\right)=5$ cm.

And the height of the cylinder is given to be $\left(h\right)=12$ cm.

So the volume of the cylinder is $V_1=\pi r^{2}h=300\pi$ cm${}^3$.

Also given the radius of the conical cavity is $r=5$ cm.

And height is also given to be $\left(h\right)=12$ cm.

So its volume is $V_2=\frac{1}{3}\pi r^{2}h=100$ cm${}^3$.

So the volume of the remaining solid is $V_1-V_2=(300-100)\pi =200\pi$ cm${}^3$.