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A company makes a greenhouse that is shaped like a rectangular prism on bottom and a half cylinder on top.

2 m
9 m
3 m
The rectangular prism has a base that is 3 x 9 m and a height of 2 m.
What is the volume of this greenhouse?

2 Answers

9 votes

Final answer:

The volume of the greenhouse is the sum of the volume of the rectangular prism and the volume of the half cylinder.

Step-by-step explanation:

To find the volume of the greenhouse, we need to find the volume of the rectangular prism and the volume of the half cylinder separately, and then add them together.

The volume of the rectangular prism is given by V = length x width x height = 9m x 3m x 2m = 54 cubic meters.

The volume of the half cylinder is given by V = 1/2 x π x r^2 x h, where r is the radius and h is the height of the cylinder. In this case, the radius is half of the width of the rectangular prism, which is 3m/2 = 1.5m, and the height is 2m. Therefore, the volume of the half cylinder is V = 1/2 x π x (1.5m)^2 x 2m = 4.5π cubic meters.

Finally, the total volume of the greenhouse is the sum of the volume of the rectangular prism and the volume of the half cylinder, which is 54 cubic meters + 4.5π cubic meters.

User Yury
by
6.3k points
10 votes

Answer: 86m cubed

Step-by-step explanation:

User Michiel De Mare
by
7.0k points