Question

sphere and a cube have equal surface areas. Show
that the ratio of the volume of the sphere to that o
cube is root 6 is to root pie


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Answer 1

Answer:

2r/l^4

Step-by-step explanation:

please check the image

Answer 2

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

Step-by-step explanation:

Given: Sphere and a cube have equal surface areas.

Find: Ratio of the volume of the sphere : cube = root 6 : root pi

Solution:

Let r be the radius of sphere and a be the side of the cube

Given, Surface area of sphere = Surface area of cube

4πr² = 6a²

(r/a)2 = 3 / 2π

r / a = √(3/2π)------------------------(1)

Volume of sphere / Volume of cube = (4/3)πr³ / a³ = (4π/3)(r/a)3 --------(2)

Substituting (1) in (2) we get:

= (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.