Question

The surface area of a solid metallic sphere is $1256c{m}^2$ it is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm ; then the no. of cones cast $(\pi =3.14)$

• A. 40
• B. 25
• C. 48
• D. 80

Answer 1

The correct option is D 80

Let the radius of the solid metallic sphere be $r$cm
$\therefore 4\pi r^2=1256$
$=>r^2=\frac{1256}{4\pi }$
$=>r\simeq 10$cm
Now,
Volume of the solid metallic sphere=$\frac{4}{3}\pi r^3$
=$\frac{4}{3}\times \frac{22}{7}\times {10}^3$
=$4190.5c{m}^3$
Volume of the solid right circular cone=$\pi r^2\frac{h}{3}$
=$\pi (2.5{)}^2\times \frac{8}{3}$
=$52.36c{m}^3$
$\therefore$ Number of cones casted=$\frac{4190.5}{52.36}$
$\simeq 80$