Question

Find the volume of the composite figure. Explain your thought, explain how your arrived at your answer. SHOW YOUR WORK FOR FULL CREDIT!

Answer 1

We assume the composite figure is a cone of radius 10 inches and slant height 15 inches set atop a hemisphere of radius 10 inches.

The formula for the volume of a cone makes use of the height of the apex above the base, so we need to use the Pythagorean theorem to find that.
   h = √((15 in)² - (10 in)²) = √115 in

The volume of the conical part of the figure is then
   V = (1/3)Bh = (1/3)(π×(10 in)²×(√115 in) = (100π√115)/3 in³ ≈ 1122.994 in³


The volume of the hemispherical part of the figure is given by
   V = (2/3)π×r³ = (2/3)π×(10 in)³ = 2000π/3 in³ ≈ 2094.395 in³

Then the total volume of the figure is
   V = (volume of conical part) + (volume of hemispherical part)
   V = (100π√115)/3 in³ + 2000π/3 in³
   V = (100π/3)(20 + √115) in³
   V ≈ 3217.39 in³