Question

a cone of height 20cm and radius of base 5 cm is made up of modelling clay . a child reshapes it in a form of a sphers . find the diameter of a sphere

Answer 1

Let r = radius of base of cone = 5 cm
Let h = height of cone = 20 cm
$\mathrm{volume}\mathrm{of}\mathrm{cone}=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\frac{1}{3}\mathrm{\pi }(5{)}^{2}20=\frac{500}{3}\mathrm{\pi }{\mathrm{cm}}^3$

Let R = radius of the sphere
$\mathrm{volume}\mathrm{of}\mathrm{sphere}=\frac{4}{3}\mathrm{\pi }{\mathrm{R}}^3$
Since cone made up of modelling clay is reshaped into sphere, so in this case volume remains constant.
Hence, volume of cone = volume of sphere
$$\begin{gathered} \Rightarrow \frac{500}{3}\mathrm{\pi }=\frac{4}{3}{\mathrm{\pi R}}^3 \\ \Rightarrow {\mathrm{R}}^3=125 \\ \Rightarrow \mathrm{R}=5\mathrm{cm} \end{gathered}$$

so, radius of the sphere = 5 cm
now, diameter of the sphere = 2(radius) = 10 cm