Question

The surface area of a solid metallic sphere is 2464 cm². It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate:

1. the radius of the sphere.
2. the number of cones recast. (Take π = `22/7`)

Answer 1

i. Total surface area of the sphere = 4πr², where r is the radius of the sphere.

Thus,

4πr² = 2464 cm²

`=> 4 xx 22/7 xx r^2 = 2464`

`=>` r² = 196

`=>` r = 14 cm

∴ R = 14 cm

ii. Volume of sphere melted = `4/3 piR^3`

= `4/3 xx pi xx 14 xx 14 xx 14`

Radius of each cone recasted = r = 3.5 cm

Height of each cone recasted = h = 7 cm

∴ Volume of each cone recasted = `1/3 pir^2h`

= `1/3 xx pi xx 3.5 xx 3.5 xx 7`

∴ Number of cones recasted

= `"Volume of sphere melted"/"Volume of each cone formed"`

= `(4/3 xx pi xx 14 xx 14 xx 14)/(1/3 xx pi xx 3.5 xx 3.5 xx 7)`

= `(4 xx 14 xx 14 xx 14)/(3.5 xx 3.5 xx 7)`

= 4 × 4 × 4 × 2

= 128