Question

The surface area of a solid metallic sphere is 616 $c{m}^2$. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed. (Use ~\pi = \frac{22}{7}).

Answer 1

Surface area of the sphere $=4\pi r^2$

$616=4\times \frac{22}{7}\times r^2$

$r^2=\frac{616\times 7}{88}=49$

$r=7cm$
Radius of the sphere is 7 cm
As sphere is melted and recast into a cone then,
Volume of the sphere = Volume of the cone

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

$\frac{4}{3}\times 7^3=\frac{1}{3}\times r^2\times 28$

$r^2=49=>r=7cm$

So, radius of the cone is 7 cm and diameter = 7 $\times$ 2 = 14 cm