I do not understand how to do this problem, please help.

Question

a hemispherical bowl of radius 8 inches is full of water. the water is poured into a vase which is a decagonal prism. the base of the vase has apothem 5 inches and side length 3 inches. how many inches deep is the water in the vase?

Answer 1

this is a volumes question. the first is a volume of a semi-sphere and the second is a volume of decagonal prism. the volume of water is the same for both.

 

volume 1 = volume 2

 

volume 1 = 0.5 x the volume of sphere

volume 1 = 0.5 x (4 x pi x R^3 / 3) = 1072.762 cubic inch

 

volume 2 = area of base x height

volume 2 = 10 x (0.5 x 5 x 3) x height = the same volume of water from the semi-sphere

 

then

1072.762 = 75 x height

height of water = 1072.762 / 75 = 14.3435 inch