Math, asked by rajashrivadkar842, 1 year ago

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

Answers

Answered by Anonymous
0

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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Answered by wifilethbridge
0

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.

https://brainly.in/question/2708996

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