Question

The ratio between 2 spheres radius is 2:3. then find out the ratio of the volume​

Answer 1

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

Step-by-step explanation:

Given :-

• The ratio between 2 spheres radius is 2:3

To find :-

• The ratio of their volumes.

Solution :-

Given that

Ratio of the radii of two spheres = 2 : 3

Let the radius of the first sphere = 2X units

Let the radius of the second sphere = 3X units

We know that

Volume of a sphere = (4/3)πr³ Cubic Units

Volume of the first sphere

= (4/3)×π×(2X)³

= (4/3)×π×8X³

= 32πX³/3 Cubic Units

Volume of the second sphere

= (4/3)×π×(3X)³

= (4/3)×π×27X³

= 108πX³/3 Cubic Units

Now,

The ratio of their volumes

= 32πX³ / 108πX³

= 32 / 108

= (4×8) / (4×27)

= 8/27

= 8:27

Answer :-

The ratio of the volumes of the two sphere is 8:27

Used Formulae:-

♦Volume of a sphere = (4/3)πr³ Cubic Units

• r = radius
• π = 22/7