Question

504 Cones each of diameter 3.5 cm and height 3 cm are melted and recast to metallic sphere. Find diameter of sphere and surface area?

Answer 1

Number of cones = 504
Diameter of cone = 3.5cm
Radius of cone = 1.75cm
Height = 3cm

Volume of each cone
=$\frac{1}{3} \times \pi \times {r}^{2} \times h$
=1/3 * 22/7 * 1.75*1.75 * 3
= 22*0.25*1.75
= 9.625 cm3

Volume of all cones = 504 *9.625= 4851 cm3

After melting,

Volume of sphere = Volume of cones

Volume of sphere = 4851
$\frac{4}{3} \times \pi \times {r}^{3} = 4851$
r^3= 1157.625
r= 10.5 cm

Diameter of sphere = 2*Radius
= 2*10. 5
= 21 cm