Question

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

Answer 1

Let the radius of sphere $=rcm$
Surface area of sphere $=4\pi r^2=2464c{m}^2$ (given)
$r^2=\frac{2464}{4\pi }$
$r^2=\frac{2464\times 7}{4\times 22}=196$
$r=14cm$.

Volume of sphere $=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (14{)}^{3}c{m}^3$
Volume of cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi (3.5{)}^2\times 7c{m}^3$
No. of cones recasted $=\frac{\text{Volume of sphere}}{\text{Volume of cone}}$
$=\frac{\frac{4\pi }{3}(14{)}^3}{\frac{1}{3}\pi (3.5{)}^2\times 7}=\frac{4\times 14\times 14\times 14}{3.5\times 3.5\times 7}=128$

The number of cones recasted is $128$