Question

a solid metallic of cone is 12 cm height and radius of its base is 3cm . It is melted and recast into a solid sphere. Find the radius of the sphere.​

Answer 1

Answer:

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Answer 2

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Given :-

Dimensions of cone

• ♡ Radius of cone, r = 3 cm
• ♡ Radius of cone, r = 3 cm♡ Height of cone, h = 12 cm

To find :-

• ◇ Radius of sphere, R

Formula used :-

$\small\bold\red{♡ Volume \: of \: cone \: = \: \frac{1 }{3}\pi \: {r}^{2} h }$

where,

♤ r = radius of cone

♤ h = height of cone

$\small\bold\red{♡ Volume \: of \: sphere \: = \frac{4}{3}\pi \: {r}^{3} }$

where

♧ r = radius of sphere.

Solution :-

Let R be the radius of sphere.

Since Cone is melted and recast in to sphere.

So, Volume of sphere = Volume of cone

$\large\bold\green{ \frac{4}{3}\pi \: {R}^{3} = \frac{1}{3}\pi \: {r}^{2} h }$

=> 4R³ = 3 × 3 × 12

=> R³ = 3 × 3 × 3

=> R = 3 cm

$\huge \fcolorbox{black}{cyan}{♛Hope it helps U♛}$