Three spheres made of copper having of 3 cm, 4cm and 5cm radii are melted and a large sphere is made.Calculate the lenghth of the large sphere.

Explanation

The radii of three smaller spheres are 3 cm, 4cm and 5cm.
`:.` the total volume of the three smaller spheres
`=(4)/(3)pi(3^(3)+4^(3)+5^(3))cc.=(4)/(3)pi(27+64+125)cc.=(4)/(3)xx(22)/(7)xx216`cc.
Let the radius of the large sphere be R cm
`:.` volume of the large sphere `=(4)/(3)xx(22)/(7)xxR^(3)`cc.
As per question,`(4)/(3)xx(22)/(7)xxR^(3)= 4/3 xx 22/7 xx 216 rArr R^3= 216 rArr R^3 = 6^3 rArr R= 6 `
Hence the radius of the large sphere = 6 cm