Question

The area of the base of a right circular cone is $314{\mathrm{cm}}^2$ and its height is $15\mathrm{cm}$. Find the volume of the cone.

Answer 1

Step 1: Given information:

The area of the base of the cone$=314{\mathrm{cm}}^2$

The height of the cone $\left(h\right)=15\mathrm{cm}$

Step 2: Calculate the base radius $\left(r\right)$ of the cone.

Since the base of the cone is in a circular shape,

$$\begin{gathered} \therefore \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{base}\mathrm{of}\mathrm{the}\mathrm{cone}=\pi r^2 \\ \Rightarrow 314=\pi r^2 \\ \Rightarrow 3.14\times r^2=314\left(\pi =3.14\right) \\ \Rightarrow r^2=\frac{314}{3.14} \\ \Rightarrow r^2=100 \\ \Rightarrow r=\sqrt{100}=10\mathrm{cm} \end{gathered}$$

Step 3: Calculate the volume of the cone.

$$\begin{gathered} \therefore \mathrm{Volume}=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h} \\ \Rightarrow \mathrm{Volume}=\frac{1}{3}\times 3.14\times {10}^2\times 15(\pi =3.14) \\ \Rightarrow \mathrm{Volume}=314\times 5 \\ \Rightarrow \mathrm{Volume}=1570{\mathrm{cm}}^3 \end{gathered}$$

Hence, the volume of the right circular cone is $1570{\mathrm{cm}}^3$.