From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and base is removed.
Question:

From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and base is removed. Find the volume of the remaining solid.

Solution:

Height of the cylinder = 10 cm
Radius of the cylinder = 6 cm
The respective heights and radii of the cone and the cylinder are the same.
∴ Volume of the remaining solid = volume of the cylinder − volume of the cone

$=\pi r^{2} h-\frac{1}{3} \pi r^{2} h$

$=\frac{2}{3} \pi r^{2} h$

$=\frac{2}{3} \times 3.14 \times 6^{2} \times 10$

$=753.6 \mathrm{~cm}^{3}$

 

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