Answer:
(75/2) in^2, or approximately 37.5 in^2
Explanation:
The equation for the volume of a cone of base area b and height h is
V = (1/3)(b)(h).
Let's solve this for b, since b is the unknown here.
Multiplying both sides of this equation by 3, we get:
3V = (b)(h), and so
b = (3V)/h
In this particular case we're given V = 75 in^3 and h = 6 in. Substituting these values into the above formula for b, we get:
3(75 in^3)
b = ------------------- = (75/2) in^2, or approximately 37.5 in^2
6 in