Question

A solid piece of metal in the form of a cuboid of dimensions 11 cm × 7 cm × 7 cm is melted to form 'n' number of solid spheres of radii `7/2` cm each. Find the value of n.

Answer 1

We know that, volume of cuboid = l × b × h

Volume of sphere = `4/3 πr^3`

Given, l = 11 cm

b = 7 cm,

h = 7 cm and r = `7/2` cm

Here, volume of cuboid = n × volume of sphere

or, 11 × 7 × 7 = `n xx 4/3 π (7/2)^3`

or, 11 × 7 × 7 = `n xx 4/3 xx 22/7 xx 7/2 xx 7/2 xx 7/2`

or, n = `(11 xx 7 xx 7 xx 3 xx 7 xx 2 xx 2 xx 2)/(4 xx 22 xx 7 xx 7 xx 7)`

or, n = 3