Question

The area of the base of a right circular cone is $\mathbf{78}\mathbf{.}\mathbf{5}\mathbf{}{\mathbf{cm}}^{\mathbf{2}}$. If its height is $\mathbf{12}\mathbf{}\mathbf{cm}$, find the volume.

Answer 1

Step 1: Given information:

The area of the base of the cone$=78.5{\mathrm{cm}}^2$

The height of the cone $(sayh)=12\mathrm{cm}$

Step 2: Calculate the base radius $(sayr)$ of the cone.

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

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{base}\mathrm{of}\mathrm{the}\mathrm{cone}=\mathrm{\pi }{r}^2 \\ \Rightarrow 78.5=\mathrm{\pi }{r}^2\left(\mathrm{\pi }=3.14\right) \\ \Rightarrow r^2=\frac{78.5}{3.14} \\ \Rightarrow r^2=25 \\ \Rightarrow r=\sqrt{25} \\ \Rightarrow r=5\mathrm{cm} \end{gathered}$$

Step 3: Calculate the volume of the cone.

$$\begin{gathered} \mathrm{Vol}.\mathrm{of}\mathrm{cone}=\frac{1}{3}\mathrm{\pi }{r}^{2}h \\ \Rightarrow V=\frac{1}{3}\times 3.14\times 5^2\times 12(\mathrm{\pi }=3.14) \\ \Rightarrow V=78.5\times 4 \\ \Rightarrow V=314{\mathrm{cm}}^3 \end{gathered}$$

Hence, the volume of the right circular cone is $314{\mathrm{cm}}^3$.