Question

if the ratio of the radius of two sphere is 3:2. find the ratio of their surface area and volumes.

plz answer step by step ​

Answer 1

Step-by-step explanation:

Given the ratio of radii of two sphere is 2:3

Let the radius of two-sphere is 2r and 3r

Then the ratio of the surface area of two spheres =4π(2r)

2

:4π(3r)

2

⇒4:9

Then ratio of volume of two spheres=

3

4

π(2r)

3

:

3

4

π(3r)

3

⇒8:27

Answer 2

let the radii be a & b.

a:b = 3:2

or

a/b= 3/2

as surface area is 4πr^2

so ratio of surface areas will be

= 4πa^2/ 4πb^2

= a^2/b^2

= (a/b)^2

= (3/2)^2 = 9/4

as volume is 4/3πr^3

so,

= {4/3πa^3} / {4/3πb^3}

= a^3/b^3

= (a/b)^3

= (3/2)^3 = 27/8