Question

Find the volume of the composite solid. Round your answer to the nearest tenth.

A composite solid is shown with a cone placed atop a cylinder. The height of the cone is 6 feet and the diameter of its base is 16 feet. The diameter of the circular bases of the cylinder are the same as the diameter of the cone. The height of the cylinder is 4 feet.

The volume is about
cubic feet.

Answer 1

1206.4 ft³

Explanation:

The volume of the composite figure is the sum of the volumes of its parts. Each part has its own volume formula.

__

formulas

The formula for the volume of a cone is ...

V = 1/3Bh . . . . where B is the area of the base, and h is the height

The formula for the volume of a cylinder is ...

V = Bh . . . . where B is the area of the base, and h is the height

The formula for the area of a circle is ...

A = πr² = π(d/2)² = (π/4)d²

Combining the volume formulas for a figure with the same base area, we have ...

V = B(cylinder height) + 1/3B(cone height)

V = B(cylinder height + 1/3×cone height) . . . . where B is the base area

composite volume

Using 16 ft for the diameter, and 4 ft and 6 ft for the heights of the cylinder and cone, respectively, we have ...

V = (π/4)(16 ft)²(4 ft + 1/3×6 ft) = 64π(4 +2) ft³ = 384π ft³

The volume is about ...

384π ft³ ≈ 1206.4 ft³