Question

If the number of square centimetres in the surface area of a sphere is equal to the number of cubic cms in its volume. Find diameter of sphere.

Answer 1

SA (sphere)=4πr²
Volume(sphere)=4/3πr³
According to the question
V=SA
4/3πr³=4πr²
1/3r³=r²
r=3cm
Hence the diameter of circle will be 3×2=6cm

Answer 2

let the radius of the sphere be r cm.then
surface area=4 pi r^2cm^2
and,volum=4/3pi r^3cm^3
according to the question,4pi r^2=4/3pi r^3
r=3
2r=6
hence the diameter of the sphere is6 cm.