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

Find the volume of the composite solid. Round your answer to the nearest tenth.-example-1
User Rchang
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1 Answer

2 votes

Answer:

67.0 cm³

Explanation:

The composite shape is a hemisphere of radius 2 atop a cylinder of height 4 and radius 2. The volume formulas for a cylinder and a sphere can be used to find its volume. (Dimensions are in centimeters.)

Hemisphere

The formula for the volume of a hemisphere is half that for the volume of a sphere:

V = (1/2)(4/3πr³) = 2/3πr³

For a radius of 2 cm, the volume is ...

V = 2/3π(2 cm)³ = 16/3π cm³

Cylinder

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

V = πr²h . . . . . . for radius r, height h

For the given dimensions, the volume is ...

V = π(2 cm)²(4 cm) = 16π cm³

Total

The total volume of the solid is the sum of these volumes:

total = hemisphere volume + cylinder volume

total = ((16/3)π +16π ) cm³ = (64/3)π cm³ ≈ 67.0 cm³

The volume of the composite solid is about 67.0 cm³.

User Joby Joseph
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