Question

A solid is in the form of one mounted on a right circular cylinder both having same radii of their bases. The base of the cone is placed on the top base of the cylinder. If the radius of the base and height of the cone be $7cm$ and $10cm$ respectively and the total height of the solid be $30cm$, find the volume of the solid.

Answer 1

Given : Radius of a cone $\left(r_1\right)=7cm$, height of the cone $\left(h_1\right)=10cm$

Height of the cylinder $\left(h_2\right)=20cm$.

Area of base of the cone $\left(b\right)=\pi r_1^2=3.14\times (7{)}^2=153.86c{m}^2$

Volume of the cone $=\frac{1}{3}\times b\times h_1$

$=\frac{1}{3}\times 153.86\times 10=512.8667c{m}^3$

Volume of the cylinder $=\pi r_1^2{h}_2$

$=3.14\times 49\times 20=3077.2c{m}^3$

Volume of the solid $=$ volume of the cone $+$ volume of a cylinder

$=512.8667+3077.2=3590.06c{m}^3$

$\therefore$ Volume of the solid $=3590.06c{m}^3$