Question

the ratio of radii of two squares is 2:3 find the ratio of their surface areas and volumes

Answer 1

4:9......8:27,.......

Answer 2

hello users.....

given that :
radii are in ratio 2:3

we have to find :
ratio in b/w surface area.
and in b/w volumes

solution:-
W.K.T
surface area of sphere = 4πr²
&
volume of sphere = 4πr³/3


now,
let ,
radius of 1st sphere = 2r
and
radius of 2nd sphere = 3r

(because ratio between radii is 2:3)

now ,
S.A of 1st sphere = 4π(2x)² = 16 πr²
and
S.A of 2nd sphere = 4π (3r)² = 36 πr²

=> ratio between their surface area
= 16πr² : 36 πr²
=> 16:36
=> 4:9 answer

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

=> Ratio between their volumes :
= 4/3 ×π(8r³) : 4/3 ×π(27r³)

=> 8:27 answer

✡✡ hope it helps ✡✡