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.
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.

Radius of the sphere = R = 15 cm

So, the volume of sphere melted

    \[=\text{ }4/3\text{ }\pi {{R}^{2}}~=\text{ }4/3\text{ x }\pi \text{ x }15\text{ x }15\text{ x }15\]

Radius of each cone recasted = r = 2.5 cm

And, height of each cone recasted = h = 8 cm

So, volume of each cone recasted

    \[=\text{ }1/3\text{ }\pi {{r}^{2}}h\text{ }=\text{ }1/3\text{ x }\pi \text{ x }2.5\text{ x }2.5\text{ x }8\]

Number of cones recasted = Volume of sphere melted/ Volume of each cone formed

Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(D) - 1

= 270