Question

From a solid cylinder whose height is $4cm$ and radius is $3cm$ a conical cavity of height $4cm$ and base radius $3cm$ is hollowed out. What is the volume of the remaining solid?
A) $9\pi c{{m}^{2}}$
B) $15\pi c{{m}^{2}}$
C) $21\pi c{{m}^{2}}$
D) $24\pi c{{m}^{2}}$

Answer 1

Hint: In this question we have been given a cylinder and hollowed a cone out of that we need to find the volume of the remaining solid. From the basic concepts we know that the volume of cylinder is given as $\pi {{r}^{2}}h$ and volume of cone is given as $\dfrac{1}{3}\pi {{r}^{2}}h$ . We need to remove the volume of the cone from the volume of the cylinder for that.

Complete step by step solution:
Now considering from the question we have been given a solid cylinder whose height is $4cm$ and radius is $3cm$ from the cylinder a cone is hollowed whose height is $4cm$ and base radius is $3cm$. Now we have been asked to find the remaining volume of the solid.
From the basic concepts we know that the volume of cylinder is given as $\pi {{r}^{2}}h$ and volume of cone is given as $\dfrac{1}{3}\pi {{r}^{2}}h$ . For answering this question we need to subtract the volume of cone from the volume of the cylinder.

The volume of solid cylinder is given as $\Rightarrow \pi {{\left( 3 \right)}^{2}}\left( 4 \right)=36\pi c{{m}^{2}}$ .
The volume conical cavity is given as $\Rightarrow \left( \dfrac{1}{3} \right)\pi {{\left( 3 \right)}^{2}}\left( 4 \right)=12\pi c{{m}^{2}}$ .
Hence we can conclude that the remaining volume of the solid is given as $\Rightarrow 36\pi c{{m}^{2}}-12\pi c{{m}^{2}}=24c{{m}^{2}}$ .
So, the correct answer is “Option D”.

Note: While answering questions of this type we should be sure with our concepts that we apply and calculations that we perform to answer this question. Similarly we have many other formulae for finding volume and surface area of different solids for example the volume of a sphere is given as $\dfrac{4}{3}\pi {{r}^{3}}$ .