Question

A hemispherical vessel is partly filled with water 12 cm deep at the lower part and oil 6 cm deep above the water. If the volume of the water is equal to the volume of the oil. What is the Volume of the oil

Answer 1

whats the radius of the hemisphere?

Answer 2

It is not given

Answer 3

so we have to assume that the vessel is full?

Answer 4

I think so

Answer 5

so the volume is 1/3(pi*h^2)(3r-h)
where r=18 and h=12

Answer 6

The answer to the question should be 8143 cu.cm

Answer 7

And the radius should be 22. But I don't know how to get 22 as the radius

Answer 8

you need the radius to work it out in the first place

Answer 9

the volume of a spherical cap is
\[V= \frac{ \pi \times h }{ 6 }(3a ^{2}+h ^{2})\]

volume of water = pi*12(3a^2 + 12^2)/6
volume of oil = volume of both oil and water - volume of water
= pi*(12+6)(3b^2 + 18^2)/6 - pi*12(3a^2 + 12^2)/6

if volume of oil = volume of water then
pi*(12+6)(3b^2 + 18^2)/6 - pi*12(3a^2 + 12^2)/6 = pi*12(3a^2 + 12^2)/6
pi*(12+6)(3b^2 + 18^2)/6 = 0

so now you can solve for b
once you find b you can get the total volume of both oil and water which is
pi*(12+6)(3b^2 + 18^2)/6
and since the two volumes are equal the volume of oil would be half the volume of both