Question

From solid cylinder whose high is 12 cm and diameter 10 cm, a colonial cavity with the same height and diameter is curved out. Find the volume of the remaining solid.

Answer 1

Given,
Diameter of cylinder = 10cm
Height of cylinder= 12cm
Radius of cylinder = 5cm

Diameter of cone= 10cm
Height of cone= 12cm
Radius of cone = 5cm

Value of pi is taken as 3.14
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$Volume \: of \: cylinder \: = \pi {r}^{2}h \\ = 3.14 \times {5}^{2} \times 12 = 942 {cm}^{3}$
$Volume \: of \: cone \: = \frac{1}{3} \pi {r}^{2}h \: \\ = \: \frac{1}{3} \times 3.14 \times {5}^{2} \times 12 = 314 \: {cm}^{3}$
$Volume \: of \: remaining \: solid \\ = Vol \: of \: cylinder \: - Vol \: of \: cone \\ = \: 942 - 314 \\ = 628 \: {cm}^{3}$