A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.

Given,

Radius of the sphere (R) = 15 cm

So, the volume of sphere melted = $\dfrac{4}{3}πR^3 = \dfrac{4}{3} \times π \times 15 \times 15 \times 15$

= 4500π cm³.

Radius of each cone formed (r) = 2.5 cm

Height of each cone (h) = 8 cm

So, volume of each cone = $\dfrac{1}{3}πr^2h = \dfrac{1}{3} \times π \times 2.5 \times 2.5 \times 8$

= $\dfrac{1}{3} \times 50π = \dfrac{50}{3}π.$

Let no. of cones formed be n.

Volume of sphere = n × Volume of cone

$\Rightarrow 4500π = n \times \dfrac{50}{3}π \\[1em] \Rightarrow n = \dfrac{4500π \times 3}{50π} \\[1em] \Rightarrow n = 270.$

Hence, no. of cones formed = 270.