Question

the diameter of a right circular cone of metal is 0.2 M and height is 40 cm a sphere is formed by melting it find the radius of the sphere

Answer 1

$Radius = \frac {Diameter}{2} \\ Radius = \frac {20}{2} = 10cm \\ \\ Volume \: of \: a \: Cone \: = \frac {1}{3} \pi {r}^{2}h \\ V = \frac {1}{3} \times \frac {22}{7} × 10 × 10 × 40 \\ V = \frac {88000}{21} {cm}^{3} \\ \\ Volume \: of \: a \: Sphere \: = \frac {4}{3}\pi {r}^{3} \\ \frac {88000}{21} = \frac {4}{3} \times \frac {22}{7} \times {r}^{3} \\ {r}^{3} = \frac {88000}{88} \\ {r}^{3} = \frac {88000}{88} \\ {r}^{3} = 1000 \\ r = 10 cm$