Question

surface area of circle and cube are esurface area of circle and cube are equal then find the ratio of their volumes ​

Answer 1

lets take circle as sphere

Let r and a be the radius of the sphere and edge of the cube respectively.

Given, Surface area of sphere = Surface area of cube

4πr2 = 6a2

(r/a)2 = 3 / 2π

r / a = √(3/2π)

Volume of sphere / Volume of cube = (4/3)πr3 / a3 = (4π/3)(r/a)3

= (4π/3)(√(3/2π))3

= (4π/3)(3/2π)(√(3/2π))

= 2√(3/2π)

= √(4x3/2π)

= √(6/π)

Thus, Volume of sphere : Volume of cube = √6 : √π.

Answer 2

We know that, Height of hemisphere = Radius of the hemisphere

∴ h = r

Volume of cylinder = πr2h = πr2 × r = πr3

Volume of cone = put formula

Volume of hemisphere = put formula 

Volume of cone : Volume of hemisphere : Volume of cylinder


equate the formula
Thus, the ratio of their volumes is 1 : 2 : 3.