Question

Aspherical cannonball 28 cm in diameter is melted and cast into a right circular cone mould, whose base in 35 cm in diameter. Find the height of the cone.

Answer 1

Sphere radius = $\frac{28}{2}$ =14 cm
volume of sphere = $\frac{4}{3}$$\pi$$r^3$
= $\frac{4}{3}$ $\times$$\frac{22}{7}$ $14\times 14\times 14$

it's melted and recast to a conical shape
it's radius = $\frac{35}{2}$ =17.5 cm
= $\frac{1}{3}$$\pi$$r^2$h
= $\frac{1}{3}$ $\times$$\frac{22}{7}$ $17.5\times 17.5\times h$

according to the question
volume of sphere = volume of cone
$\frac{4}{3}$ $\times$$\frac{22}{7}$ $14\times 14\times 14$ = $\frac{1}{3}$ $\times$$\frac{22}{7}$ $17.5\times 17.5\times h$
3658.6 = 102.08 $\times$h
$\frac{3658.6}{102.08}$=h
35.84 = h