Tsa of sphere and cube is same show that the ratio of volume of cube to sphere is root of 11: root of 6
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TSA of sphere = 4πr²
TSA of cube = 6a²
A/q,
4πr²= 6a²
⇒a²/r²= 2π/3
⇒a/r =√(2π/3)______(1)
now, ratio of volume,
(a³)/[(4/3)×πr³]= (3a³)/(4πr³)
from equation (1),
ratio= [(3/4π)]×(√2π/3)³ = √π :√6
TSA of cube = 6a²
A/q,
4πr²= 6a²
⇒a²/r²= 2π/3
⇒a/r =√(2π/3)______(1)
now, ratio of volume,
(a³)/[(4/3)×πr³]= (3a³)/(4πr³)
from equation (1),
ratio= [(3/4π)]×(√2π/3)³ = √π :√6
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