Question

The surface areas of two spheres are in the ratio 16:9 . The ratio of their volume is

Answer 1

Step-by-step explanation:

s1/s2= 16/9

r1= 4 and r2 =3

v1/v2= 64/27

Answer 2

✬ Ratio of Volume = 64 : 27 ✬

Step-by-step explanation:

Given:

• Surface area of two spheres are in ratio 16 : 9.

To Find:

• What is the ratio of their volumes ?

Solution: Let the radius of first and second sphere be R & r respectively.

As we know that

★ Surface Area of Sphere = 4πr² ★

• S.A of first sphere = 4πR²
• S.A of second sphere = 4πr²

A/q

$\implies{\rm }$ (4πR²) : (4πr²) = 16 : 9

$\implies{\rm }$ 4πR²/4πr² = 16/9

$\implies{\rm }$ R²/r² = 16/9

$\implies{\rm }$ R/r = √16/√9

$\implies{\rm }$ R/r = 4/3

So,

➳ Radius of first sphere is R = 4 and

➳ Radius of second sphere is r = 3.

Now,

★ Volume of Sphere = 4/3πr³ ★

• Vol. of 1st sphere = 4/3πR³
• Vol. of 2nd sphere = 4/3πr³

$\implies{\rm }$ (4/3πR³) : (4/3πr³)

$\implies{\rm }$ (4/3πR³) / (4/3πr³)

$\implies{\rm }$ R³/r³ { Put values of Radius }

$\implies{\rm }$ 4³/3³

$\implies{\rm }$ 64/27

$\implies{\rm }$ 64 : 27

Hence, The ratio of volume of two spheres is 64 : 27.