Answer:
301.6 ft³
Step-by-step explanation:
The volume (V) of a cone is calculated using the formula
V = [tex]\frac{1}{3}[/tex] × area of base × perpendicular height (h)
h can be calculated by using Pythagoras' identity in the right triangle
with hypotenuse = 10 and legs 6 and h, thus
h² + 6² = 10²
h² + 36 = 100 ( subtract 36 from both sides )
h² = 64 ( take the square root of both sides )
h = [tex]\sqrt{64}[/tex] = 8
Hence
V = [tex]\frac{1}{3}[/tex] × π × 6² × 8
= [tex]\frac{1}{3}[/tex] × 288π = [tex]\frac{288\pi }{3}[/tex] ≈ 301.6
