2. Metallic spheres of radius 6
eres of radius 6 cm., 8 cm. and 10 cm, respectively are melted to form a
ole solid sphere. Find the radius of the resulting sphere.
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vol.of 1st sphere= 4/3 x pie r^3
= 4/3 x 22/7 x 6 x 6 x 6
= 216 x 4/3 x 22/7 cm^3 .......(i)
vol.of 2nd sphere= 4/3 x 22/7 x 8 x 8 x 8
= 512 x 4/3 x 22/7 cm^3 .......(ii)
vol.of 3rd sphere= 4/3 x 22/7 x 10 x 10 x 10 ........(iii)
= 1000 x 4/3 x 22/7 cm^3 ........(iii)
Vol.of big sphere= (1000 + 512 + 216) x 22/7 x 4/3 ........(iv)
After melting vol.of big circle formed=4/3 x 22/7 x r^3
---> (1000 + 512 + 216) x 22/7 x 4/3 =4/3 x 22/7 x r^3 ( from (i), (ii), (iii) and (iv) )
--->1000 + 512 + 216 = r^3
--->1728 = r^3
--->12 = r
therefore radius of the final sphere is 12cm
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