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
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.