Question

The radius of a spherical iron ball is 15 cm . It is melted and recast in to conical bullets

of radius 3cm and height 5 cm. How many such cones can be obtained ?​

Answer 1

SOLUTION :-

Let the number of conical bullets be x.

Volume of the spherical iron ball = $\sf\dfrac{4}{3}\pi r^3$

                                                       = $\sf\dfrac{4}{3}\times \pi \times 15 \times 15 \times 15$

                                                       = $\sf 4\times \pi \times 5 \times 15 \times 15$

                                                       = $\sf 4500 \pi$

Volume of one conical bullet = $\sf\dfrac{1}{3}\pi r^2h$

                                                = $\sf\dfrac{1}{3}\times \pi \times 3 \times 3 \times 5$

                                                = $\sf\pi \times 3 \times 5$

                                                = $\sf 15\pi$

According to the question,

Volume of the spherical iron ball = x × Volume of one conical bullet

$\longrightarrow \sf 4500\pi = x\times 15\pi \\\\\longrightarrow x=\dfrac{4500\pi}{15\pi}\\\\\longrightarrow \bf x = 300$

Number of conical bullets = 300