Question

(2) The diameter of a right circular cone of metal is 0.2 m and height is 10 cm. A sphere is formed bymelting it. Find the radius of the sphere.​

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Radius=6.29\:cm}}$

${\bold{\underline{\underline{Step-by-step\:explanation}}}}$

$\underline \bold{Given : } \\ \implies Diameter \: of \: cone =0.2 \: m \\ \\ \implies Height \: of \: cone = 10 \: cm \\ \\ \underline \bold{To \: Find: } \\ \implies Radius \: of \: sphere = ?$

• According to given question :

$\bold{Using \: formula \: of \: Volume \: of \: cone : } \\ \implies Volume \: of \: cone = \frac{1}{3} \pi {r}^{2} h \\ \\ \implies Volume = \frac{1}{3} \times \pi \times {10}^{2} \times 10 \\ \\ \implies Volume = \frac{1}{3} \times \pi \times 1000 \\ \\ \bold{\implies Volume = \frac{1000\pi}{3} } \\\\\bold{Volume\:of\:cone=Volume\:of\:sphere}\\ \\ \bold{Using \: formula \: of \: Volume \: of \: sphere : } \\ \implies Volume \: of \: sphere = \frac{4}{3} \pi {r}^{2} \\ \\ \implies \frac{1000\pi}{3} = \frac{4}{3} \pi {r}^{3} \\ \\ \implies 1000 \times \pi = 4 \times \pi \times {r}^{3} \\ \\ \implies {r}^{3} = \frac{1000 \times \pi}{4 \times \pi} \\ \\ \implies r = \sqrt[3]{250} \\ \\ \bold{\implies r = 6.29\: cm}$

Answer 2

Diameter of a right circular cone = 0.2m = 20cm

Radius of the cone = 20/2 = 10cm

Height of the cone = 10cm

Volume of the cone = 1/3 × πr^2h

πr^2h= 1/3 × π× 10 × 10 × 10

= 1000π/3

Volume of the sphere = 4/3πr^3

Since the sphere is formed by melting the cone ,

Therefore,

Volume of cone = Volume of sphere

1000π/3= 4/3 × π × r^3

r^3 = 1000π/4π

r^3 = 250

r = 6.3cm approx.