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.

Area of the base of the right circular cone$=314{\mathrm{cm}}^2$

Height of cone $\left(h\right)=15\mathrm{cm}$

Step 2: Calculate the radius of the base of the circular cone.

Area of circle of radius $r$ is,

$A=\mathrm{\pi }{r}^2$

Since the base of the cone has a circular shape,

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

Step 3: Calculate the volume of the cone.

$$\begin{gathered} \mathrm{Volume}=\frac{1}{3}\mathrm{\pi }{r}^{2}h \\ \Rightarrow \mathrm{Volume}=\frac{1}{3}\times 3.14\times {\left(10\right)}^2\times 15 \\ \Rightarrow \mathrm{Volume}=\frac{4,710}{3} \\ \therefore \mathrm{Volume}=1,570{\mathrm{cm}}^3 \end{gathered}$$

Hence, the volume of the cone is $1,570{\mathrm{cm}}^3$.