Question

Volume of two sphere are ratio 24:27
ratio of their radii are
please answer in clear steps​

Answer 1

Correct Question : Ratio of volume of two sphere is 64 : 27. Find the ratio of their radii.

Solution :-

Given : Volume of two sphere are ratio 64 : 27

We know that,

Volume of sphere = 4/3 πr³ cubic unit

Volume of first sphere / Volume of second sphere

=> 4/3 πR³ / 4/3 πr³ = 64/27

=> R³/r³ = 64/27

=> R³/r³ = 4³/3³

=> R/r = 4/3

Hence,

Ratio of their radii = 4 : 3

Answer 2

Answer:

Volume of sphere = 4/3 π r ^3

let radius of sphere 1 be r and sphere 2 be R

then vol of sphere 1 ÷ vol of sphere 2 = 64÷27

=> 4/3 π r^3 ÷ 4/3 π R^3 = 64÷ 27

by cross multiplying

=>4/3 π r^3 × 27= 4/3 π R^3 ×64

=> r^3 ×27 = R^3×64

=> (r/R)^3 = 64/27

=> r/R = cuberoot of 64/27

=>r:R = 4:3