Question

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

Answer 1

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.