Question

surface area s of sphere and cube are equal then find the ratio of their volumes​

Answer 1

Answer:

given: surface area of a cube = surface area of sphere

let a side of the cube = a, radius of sphere = r.

Cube: SA = 6a^2

Sphere: SA = 4pi×r^2

=> r^2 = 6a^2/(4pi) = 3a^2/2pi

= 0•477a^2 => r = sqrt(0•477 a^2)

apx = 0•69a.

Volume:

Cube = a^3

sphere = 4/3 * pi * r^3 = 4•2(0•69a)^3 = 4•2×0•69^3*a^3 = apx 1•376a^3

ratio of volume of the cube : the sphere = a^3 : 1•376a^3

= 1:1•376 (dividing by a^3)

rationalize: = 8*1:8*1•376=8 : 11•008

ratio of volume of the cube : volume of the sphere is

apx = 8 : 11

Hope this will help you

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