Question

A solid metallic cylinder of radius 9cm and height 36cm is melted and recast into 81 equal sphere. Find the radius of sphere

Answer 1

According to Question,

Volume of cylinder= 81 Spheres

$= > \pi {r1}^{2}h = 81 \times \frac{4}{3}\pi {r}^{2} \\ \\ = > 9 \times 9 \times 36 = 81 \times \frac{4}{3} \times {r}^{3} \\ \\ = > \frac{ 81 \times 36 \times 3}{4 \times 81} = {r}^{3} \\ \\ = > {r}^{3} = 9 \times 3 \\ \\ = > {r}^{3} = {3}^{3} \\ \\ = > r = 3cm$

Thus the required radius of the sphere is. 3cm

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Answer 2

The radius of sphere is 3 cm

Step-by-step explanation:

Radius of cylinder = 9 cm

Height of cylinder = 36 cm

Volume of cylinder =$\pi r^2 h = \pi \times 9^2 \times 36$

We are given that A solid metallic cylinder of radius 9cm and height 36cm is melted and recast into 81 equal sphere

Volume of sphere =$\frac{4}{3} \pi r^3$

$\pi \times 9^2 \times 36 =81 \times \frac{4}{3} \pi r^3$

$9^2 \times 36 =81 \times \frac{4}{3} r^3$

$\frac{9^2 \times 36}{81 \times \frac{4}{3}}=r^3$

$\sqrt[3]{\frac{9^2 \times 36}{81 \times \frac{4}{3}}}=r$

3=r

Hence The radius of sphere is 3 cm

#Learn more:

A metallic solid sphere of sphere of radius 4.2cm is melted and recast into the shape of a solid cylinder of radius 6cm .find the height of the cylinder.

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