Question

I need help finding the Volume of the smaller sphere to the larger sphere

Answer 1

Hey there!!

The formula to find the surface area of a sphere  4πr²

1 st sphere = surface area = 9π

9π = 4πr²

4r² = 9

r² = 9/4

r = √9/4

r = 3/2

The radius of the first sphere = 3/2

The second sphere :

Surface area = 25π

4πr² = 25π

4r² = 25

r² = 25/4

r = √25/4

r = 5/2

The radius of the second sphere = 5/2

Volume of a sphere formula - 4/3 ( πr³ )

Let's find the volume of the first sphere

Radius = 3/2

Plug in the value

4/3 ( π × (3/2)³ )

4/3 ( π × 27/8)

9π/2 = volume of the first sphere

Let's find the volume of the second sphere :

Radius = 5/2

4/3 ( π × ( 5/2 )³ )

4/3 ( π × 125 / 8 )

125π/6 = volume of the first sphere

Ratio of 1st sphere to the second sphere

( 9π/2 ) ÷ ( 125π/6 )

= 27 : 125 is the ratio

Hope my answer helps!

Answer 2

The hint tells you how to do it.

r1/r2 = √(a1/a2) = √(9π/(25π)) = 3/5

v1/v2 = (r1/r2)³ = (3/5)³ = 27/125

smaller volume : larger volume = 27 : 125