Question

A cone of height 24cm and radius of base 6cm is made up of modelling clay. a child reshaped it in

the form of a sphere. Find the radius of the sphere.

Answer 1

$Given:\\\\Cone:\\h=24cm\\r=6cm\\Sphere:\\R=?\\\\Solution:$

Volume of cone = Volume of sphere

$\frac{1}{3}\pi r^2h=\frac{4}{3} \pi R^3$

It is because no extra clay is used nor clay is added so the amount of clay will remain constant and hence volume will be equal.

$\frac{1}{3}\pi *(6)^2*24=\frac{4}{3}\pi R^3\\\\4R^3=36*24\\R^3=9*24\\R^3=216cm\\R=6cm$

Hence, the radius of sphere of sphere is 6 cm.

Hope it helps u.....   :D

Answer 2

$\frak \red{Question :}$

• A cone of height 24cm and radius of base 6cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

______________________________________

$\frak \blue{Solution :}$

$\sf{Volume \: of \: cone =} \frak{ \frac{1}{3} \times \pi \times 6 \times 6 \times 24 {cm}^{3} }$

• $\sf{If \: r \: is \: the \: radius \: of \: the \: sphere, then \: it's \: volume \: is} \: \frak{ \frac{4}{3} \pi {r}^{3} }$

Since, the volume of clay in the form of the cone and the sphere remains the same, we have

• $\frak{ \frac{4}{3} \times \pi \times {r}^{3} = \frac{1}{3} \times \pi \times 6 \times 6 \times 24}$

• $\frak{ {r}^{3} = 3 \times \times 24 = {3}^{3} \times {2}^{3} }$

• $\frak{ r = 3 \times 2 = 6}$

$\sf \pink{Therefore, \: the \: radius \: of \: the \: sphere \: is \: 6cm.}$