Surface area of a sphere A is 300% more than the surface area of another sphere B. If the volume of sphere B is p% less than the volume of sphere A, find the value of 'p'.
Answers
Answered by
5
Surface area of a sphere is given by 4 x Pi x r² where Pi = 22/7 and r = radius of sphere.
In the given problem, we can deduce that Ra = Rb√3; where Ra = radius of sphere A and Rb = radius of sphere B.
Moving to the volume of sphere given by 4/3(Pi)(r³)
Volume of sphere A = 4/3(Pi)(Ra³) = 4/3 x (Pi) x {(Rb√3)³} because as we found out above Ra = Rb√3.
Similarly, Volume of sphere B = 4/3(Pi)(Rb³)
In order to find the ratio of volumes we must divide volume of sphere B by volume of sphere A.
Therefore, [4/3(Pi)(Rb³)] ÷ [4/3 x (Pi) x {(Rb√3)³}]
Everything else cancels out and we are left with 1 ÷ 3√3 = 1 ÷ 5.196 =0.1924
Or in other words 19.24%.
It will be safe to say that the Volume of Sphere B is 80.76% (i.e. 100-19.24) less than the volume of Sphere A.
Hence value of p will be 80.76.
In the given problem, we can deduce that Ra = Rb√3; where Ra = radius of sphere A and Rb = radius of sphere B.
Moving to the volume of sphere given by 4/3(Pi)(r³)
Volume of sphere A = 4/3(Pi)(Ra³) = 4/3 x (Pi) x {(Rb√3)³} because as we found out above Ra = Rb√3.
Similarly, Volume of sphere B = 4/3(Pi)(Rb³)
In order to find the ratio of volumes we must divide volume of sphere B by volume of sphere A.
Therefore, [4/3(Pi)(Rb³)] ÷ [4/3 x (Pi) x {(Rb√3)³}]
Everything else cancels out and we are left with 1 ÷ 3√3 = 1 ÷ 5.196 =0.1924
Or in other words 19.24%.
It will be safe to say that the Volume of Sphere B is 80.76% (i.e. 100-19.24) less than the volume of Sphere A.
Hence value of p will be 80.76.
Answered by
3
Answer:
Step-by-step explanation:
Attachments:
Similar questions