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 the number of cones recast.

• A. 256
• B. 128
• C. 64
• D. 32

Answer 1

The correct option is B

128

Let the radius of the sphere be R.

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 (R) = 14 cm

Sphere is melted and recast into solid cones.
Number of cone $=\frac{Volumeofthesphere}{Volumeofthecone}$
$=\frac{\frac{4}{3}\pi R^3}{\frac{1}{3}\pi r^{2}h}=\frac{4R^3}{r^{2}h}$
$=\frac{4\times 14\times 14\times 14}{3.5\times 3.5\times 7}=128$