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3 years ago

Find the volume of the composite space figure to the nearest whole number.

Mathematics

1 answer:

Romashka [77]3 years ago

7 0

Answer:

d. 944 mm^3

Step-by-step explanation:

The area of a circle is given by ...

A = πr² . . . . . where r is the radius, half the diameter

The area of a circle with diameter 9 mm is ...

A = π(4.5 mm)² = 20.25π mm²

The area of the semi-circular end of the prism is half this value, or ...

semicircle area = (1/2)(20.25π mm²) = 10.125π mm² ≈ 31.809 mm²

The area of the rectangular portion of the end of the prism is the product of its width and height:

A = wh = (9 mm)(6 mm) = 54 mm²

Then the base area of the prism is ...

base area = rectangle area + semicircle area

= (54 mm²) +(31.809 mm²) = 85.809 mm²

This base area multiplied by the 11 mm length of the prism gives its volume:

V = Bh = (85.809 mm²)(11 mm) ≈ 944 mm³

The volume of the composite figure is about 944 mm³.

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