How to calculate the volume of a sphere based on percentage of surface area?

How would you calculate the volume of a sphere based off of a percentage of the surface area if the volume of the sphere is known but only in terms of the surface area?



Example:



A sphere is measured to displace 280,000 cm^3 of water but its surface area is only submerged 72% under water. What is the total volume of the sphere?



Please show work and explain and you will receive points.How to calculate the volume of a sphere based on percentage of surface area?
First the formula for the volume of a sphere is:



V = (4/3)(pi)(r^3), and the area of a sphere is:



A = 4*(pi)(r^2), which makes it possible to rewrite the two formulae as:



V = 4/3(pi)(r^3) = 1/3(A*r) and



A = 3(V/r)



Now, i know that having 72% of the sphere submerged is multiplying the A by .72.



280000 = 1/3(.72A*r)



Solving for A, you get:



A = 3*280000/(r*.72) and then equate that to A = (3V)/r



(3*280000)/(.72r) = (3V)/(r)



280000/.72 = V



V = 388,888.88888 cm^3How to calculate the volume of a sphere based on percentage of surface area?
V = 383,561.6 cm^3

apa 6th edition

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