Question

The radii of two spheres are in the ratio 2:3 find the ratio of their surface areas and ratio of their volumes.

Answer 1

hello users ...
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we have given that:
the radius of spheres are in ratio 2:3

we have to find :
(1.) Ratio between their Surface area
(2.) Ratio between their Volume

solution:-
we know that:
(1.) Surface area of sphere = 4πr²
(2.) volume of sphere = 4/3×πr³

Here,
the radii are in ratio 2:3
=> let radius of 1st sphere = 2r
and
radius of 2nd sphere = 3r

now
1. S.Area of 1st sphere = 4π(2r)²
and
S.Area of 2nd sphere = 4π(3r)²

=>Ratio = 4π(2r)² / 4π(3r)²

=> 2² / 3²

=> 4:9 answer

now,
Ratio between their Volumes

2. volume of 1st sphere = 4/3×π (2r)³
and
volume of 2nd sphere = 4/3×π (3r)³

=>Ratio = 4/3×π(2r)³ / 4/3×π(3r)³

=> 2³ / 3³

=> 8:27 answer
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⭐✡ hope it helps :)

Answer 2

Answer:

Given: Radii of two Spheres is 2:3

To find: Ratio of SA and Volume

∴ Ratio of SA = 4πr2(1) = 4πr2(2)

                      = r2(1) = r2(2)

= (2)2 = (3)2

= 4:9

= r3(3) = r3(2)

= (2)2 = (3)3

= 8:27