Question

A solid is in the form of a cone mounted on a right circular cylinder both having same radii of their bases. 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 4 cm and 7 cm, respectively, and the height of the cylindrical part of the solid is 3.5 cm, the volume of the solid is equal to

• A. $293\frac{1}{3}c{m}^3$
• B. $293\frac{1}{5}c{m}^3$
• C. $298\frac{1}{3}c{m}^3$
• D. $298\frac{1}{5}c{m}^3$

Answer 1

The correct option is A $293\frac{1}{3}c{m}^3$

Volume of the solid $=$ Volume of the cylindrical part $+$ Volume of conical part
Volume of a Cylinder of Radius $R$ and height $h$ $=\pi R^{2}h$

Volumeof a cone $=\frac{1}{3}\pi r^{2}h$ where $r$ is radius and $h$ is height of the cone.
Hence, Volume of the solid

$=\frac{22}{7}\times 4\times 4\times 3.5+\frac{1}{3}\times \frac{22}{7}\times 4^2\times 7=176+\frac{352}{3}=293\frac{1}{3}{cm}^2$