Question
From a solid right circular cylinder with height $10\ cm$ and radius of the base $6\ cm,$ a right circularcone of the same height and same base is removed. Find the volume of the remaining solid.
✓
Answer
Height of the cylinder $(h)=10 cm$ and radius of the base $(r)=6 cm$
Volume of the cylinder $=\pi r^2 h$
Height of the cone $=10 cm$
Radius of the base of cone $=6 cm$
Volume of the cone $=\frac{1}{3} \pi r^2 h$
Volume of the remaining part
$ =\pi r^2 h-\frac{1}{3} \pi r^2 h$
$=\frac{2}{3} \pi r^2 h$
$=\frac{2}{3} \times \frac{22}{7} \times 6 \times 6 \times 10$
$=\frac{5280}{7}$
$=754 \frac{2}{7} cm ^3 $
Volume of the cylinder $=\pi r^2 h$
Height of the cone $=10 cm$
Radius of the base of cone $=6 cm$
Volume of the cone $=\frac{1}{3} \pi r^2 h$
Volume of the remaining part
$ =\pi r^2 h-\frac{1}{3} \pi r^2 h$
$=\frac{2}{3} \pi r^2 h$
$=\frac{2}{3} \times \frac{22}{7} \times 6 \times 6 \times 10$
$=\frac{5280}{7}$
$=754 \frac{2}{7} cm ^3 $
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