Answer:
The desired radius is r = 7.5 inches
Step-by-step explanation:
The formula for the volume of a sphere of radius r is V = (4/3)πr³. A hemisphere is half a full sphere, so the formula for the volume of a hemisphere of radius r is (4/3)(1/2)πr³, or (2/3)πr³.
We know that the volume of the hemisphere is 885 in³:
885 in³ = (2/3)πr³ and need to solve this first for r³ and then for r.
This is equivalent to:
885 in³ = (2π/3)r³.
We can now isolate r³ by multiplying both sides of this equation by (3 / [2π]):
(3 / [2π])(885 in³) = (3 / [2π])(2π/3)r³ = r³
Then r³ = 422.556 in³
Finally, we find the desired hemisphere radius by taking the cube root of both sides of the above equation:
r = ∛(422.556 in³) = 7.5 in (which is to the nearest tenth of an inch)
The desired radius is r = 7.5 inches
