Question

The total area of a solid metallic sphere is 1256 cm². It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate :

1. the radius of the solid sphere.
2. the number of cones recast. [Take π = 3.14]

Answer 1

Total area of solid metallic sphere = 1256 cm² 

i. Let radius of the sphere is r then 

4πr² = 1256 

`=> 4 xx 22/7r^2 = 1256`

`=> r^2 = (1256 xx 7)/(4 xx 22)`  

`=> r^2 = (157 xx 7)/11` 

`=> r^2 = 1099/11` 

`=> r = 1099/11` 

`=> r = sqrt(99.909) = 9.995  cm`

`=>` r = 10 cm

ii. Volume of sphere = `4/3pir^3`

= `4/3 xx 22/7 xx 10 xx 10 xx 10`

= `88000/21 cm^3` 

Volume of right circular cone = `1/3pir^2h`

= `1/3 xx 22/7 xx (2.5)^2 xx 8`

= `1100/21 cm^3` 

Number of cones 

= `88000/21 ÷ 1100/21` 

= `88000/21 xx 21/1100` 

= 80