Question

The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :

1. radii,
2. surface areas. 

Answer 1

Volume of first sphere = 27 × volume of second sphere

Let radius of first sphere = r₁

And radius of second sphere = r₂ 

Therefore, volume of first sphere = `4/3pir_1^3` 

And volume of second sphere = `4/3pir_2^3` 

i. Now, according to the question 

= `4/3pir_1^3`

= `27 xx 4/3pir_2^3` 

`r_1^3 = 27r_2^3 = (3r_2)^3`

`=>` r₁ = 3r₂

`=> r_1/r_2 = 3/1` 

∴ r₁ : r₂ = 3 : 1 

ii. Surface area of first sphere = `4pir_1^2` 

And surface area of second sphere = `4pir_2^2` 

Ratio in surface area = `(4pir_1^2)/(4pir_2^2)`

= `r_1^2/r_2^2`

= `3^2/1^2`

= `9/1`

= 9 : 1