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