To find the volume of the composite space figure, we need to find the volume of the rectangular prism and half cylinder separately, and then add them together.
The volume of a rectangular prism is found by multiplying its height, depth, and width. So, the volume of the rectangular prism is 6mm * 11mm * 9mm = 594mm3.
The volume of a half cylinder is found by multiplying its base area (which is the area of a circle with a radius equal to the width of the rectangular prism) by its height (which is half the height of the rectangular prism). The base area of a circle can be found using the formula A = πr^2, where r is the radius. In this case, the radius is 9mm/2 = 4.5mm. So, the base area is π(4.5mm)^2 = 63.59mm2. The height of the half cylinder is 6mm/2 = 3mm. Therefore, the volume of the half cylinder is 63.59mm2 * 3mm = 190.77mm3.
Finally, we add the volumes of the rectangular prism and the half cylinder: 594mm3 + 190.77mm3 = 784.77mm3.
Rounded to the nearest whole number, the volume of the composite space figure is 785 mm3.
Therefore, the correct answer is not given in the options provided.
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
944 mm 3
1 answer
3 answers