Question

The surface area of a solid metallic sphere is $2464c{m}^2$. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate:
i) The radius of the sphere
ii) The number of cones recast. (Take $\pi =\frac{22}{7}$) [4 MARKS]

Answer 1

Each Part: 2 Marks

i) Surface area of a solid metallic sphere $=2464c{m}^2$
$\Rightarrow 4\pi R^2=2464$
$\Rightarrow 4\times \frac{22}{7}\times R^2=2464\Rightarrow R^2=196$
$\Rightarrow R=14$
Radius of the sphere = 14 cm

ii) Sphere is melted and recast into solid cones
No. of cone $=\frac{Volumeofthesphere}{Volumeofthecone}$
$=\frac{\frac{4}{3}\pi R^3}{\frac{1}{3}\pi r^{2}h}=\frac{4R^3}{r^{2}h}$
$=\frac{4\times 14\times 14\times 14}{3.5\times 3.5\times 7}=128$