Question

The radius of the base of a cylinder is 7 cm and its height is 10 cm. A cone with the same radius as that of the base of the cylinder and a height of 6 cm is placed on the cylinder. What is the volume of the solid formed?

Answer 1

The given figure consists of a cone and a cylinder.
Radius of the base of the cylinder = 7 cm
Height of the cylinder = 10 cm
Volume of a cylinder = πr²h
Volume = π × 49 × 10 = 1540 cm³

∴ Volume of the cylinder = 1540 cm³
Radius of the base of the cone = 7 cm
Height of the cone = 6 cm
Volume of a cone =$\frac{1}{3}\mathrm{\pi }{r}^{2}h$
Volume = $\frac{1}{3}\mathrm{\pi }\times 7^2$ × 6 = 308 cm³
Volume of the cone = 308 cm³
Total volume = Volume of the cylinder + Volume of the cone
= ( 1540 + 308) cm³ = 1848 cm³
∴ Total volume of the given figure = 1848 cm³