Question

Anderson’s nursery was choosing between two different greenhouses. 2 greenhouses have a rectangular prism base with a length of 12 meters, width of 12 meters, and height of 10 meters. greenhouse 1 has a square pyramid top with a base of 12 meters by 12 meters and height of 8 meters. greenhouse 2 has a triangular prism top. the triangular sides have a base of 12 meters and height of 8 meters. the prism has a height of 12 meters. which statements are true about the greenhouses? select two options. the space inside greenhouse 1 can be found using the equation v = 12 (12) (10) one-half (12) (12) (8). the space inside greenhouse 1 can be found using the equation v = 12 (12) (10) one-third (12) (12) (8). the space inside greenhouse 2 can be found using the equation v = 12 (12) (10) one-half (12) (12) (8). the space inside greenhouse 2 can be found using the equation v = 12 (12) (10) one-third (12) (12) (8). the space inside greenhouse 1 is 192 meters cubed greater than the space inside greenhouse 2.

Answer 1

The statements that are true about the volume of the greenhouses are: B and E.

What is the Volume of Rectangular Prism and Pyramid?

Volume of rectangular prism = (length)(width)(height)

Volume of rectangular pyramid = 1/3(length)(width)(height)

Volume of Greenhouse 1 = volume of rectangular prism + volume of rectangular pyramid = (12)(12)(10) + 1/3(12)(12)(8) = 1,824 m³

Volume of Greenhouse 2 = volume of rectangular prism + volume of triangular prism = (12)(12)(10) + 1/2(12)(8)(12) = 2,016 m³

Difference between the spaces in both greenhouses = 2,016 - 1,824 = 192 m³

Therefore, the true statements about the greenhouses are: Option B and Option E.

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