Question

If surface area of a sphere and cube are equal, then find the ratio of their volumes.

Answer 1

Hi ,

Let radius of the Sphere = r

length of the side of a cube = a

It is given that ,

Surface area of a Sphere and Cube

are equal.

4πr² = 4a²

r²/a² = 4/( 4π )

( r/a )² = 1/π

r/a = √1/π ---( 1 )

ratio = ( sphere volume )/( cube volume )

= [ ( 4/3)πr³ ]/( a³ )

= ( 4π )/3 × ( r/a )³

= ( 4π/3 ) × ( 1/√π )³ { from ( 1 ) }

= ( 4π/3 ) × 1/( π√π )

= 4/(3√π )

= 4 : 3√π

Therefore ,

ratio of volume = 4 : 3√π

I hope this helps you.

: )