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

Question

A rectangular prism has a height of 6mm, depth of 11mm and width of 9mm. A half cylinder is shown on top of the rectangular prism. The image label reads 'Not drawn to scale'.
(1 point)
Responses

416 mm3
416 mm 3

705 mm3
705 mm 3

1,294 mm3
1,294 mm 3

944 mm3

Answer 1

To find the volume of the composite space figure, we first need to calculate the volume of the rectangular prism and then of the half cylinder.

Volume of rectangular prism = height x depth x width = 6mm x 11mm x 9mm = 594 mm³

Volume of half cylinder = 1/2 x π x radius² x height
The radius would be half of the width of the rectangular prism, so the radius is 4.5mm.
Volume of half cylinder = 1/2 x π x 4.5mm x 4.5mm x 6mm = 228.5 mm³

Total volume = Volume of rectangular prism + Volume of half cylinder
Total volume = 594 mm³ + 228.5 mm³ = 822.5 mm³

The volume of the composite space figure is 822 mm³ rounded to the nearest whole number.