Question

The radii of two spheres are in the ratio 2:5.
Find the ratio between their surface area-​

Answer 1

Step-by-step explanation:

9th

Maths

Surface Areas and Volumes

Volume of a Sphere

The ratio of radii of two s...

MATHS

avatar

Asked on December 26, 2019 by

Keerthana Gosalia

The ratio of radii of two spheres is 2 : 3. Find the ratio of their surface areas and volumes.

MEDIUM

Help best friend

Study later

ANSWER

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

Answer:

4 : 25

Step-by-step explanation:

We know that surface area of a sphere = 4 * π * radius²

Let the measure of the two radii be 2x and 5x

So surface area of the sphere with radius 2x = 4 * π * (2x)²

= 4 * π * 4x²

= 16πx²

Surface area of the sphere with radius 5x = 4 * π * (5x)²

= 4 * π * 25x²

= 100πx²

Ratio of the surface area = (16πx²) / (100πx²)

= 16 / 100

= 4 / 25

Therefore the ratio  of the surface area of the two spheres is 4 : 25