Question

The surface area of two spheres are in the ratio 16:9.then find the ratio of their volumes

Answer 1

Solution

Given :-

• Ratio of Surface area = 16 : 9

Find :-

• Ratio of their Volume

Explanation

Using Formula

★Surface area of Sphere = 4πr²

★ Volume of Sphere = 4/3 πr³

Now, For first sphere

• Radius = r
• Surface area = SA

So, Now

==> Surface area of first sphere (SA) = 4πr²

For, Second sphere

• Radius = r'
• Surface area = (SA')

So, Now

==> Surface area of second sphere (SA') = 4πr'²

According to question,

==> (SA) : (SA') = 16 : 9

==> 4πr²/4πr'² = 16/9

==> r²/r'² = 16/9

==> (r/r'²) = (4/3)²

==> r/r' = 4/3 ________________(1)

Again,

For First Sphere

• Volume = V

So,Now

==> Volume of first sphere = 4/3 πr³

For second sphere

• Volume = V'

So,Now

==> Volume of second sphere = 4/3 πr'³

Now, calculate Ratio of their

==> (V) : (V') = (4/3 πr³( : (4/3 πr'³)

==> V : V' = r³ : r'³

Or,

==> V /V' = r³/r'³

Or,

==> V/V' = (r/r')³

Keep value by equ(1)

==> V/V' = (4/3)³

==> V/V' = 64/27

Hence

• Ratio of their volume will be 64 : 27

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