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

Answer:

B and C

Step-by-step explanation:

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Answer 2

Applying the appropriate volume formula for the square pyramid and prism, the statements that are true are: B and E.

What is the Volume of Square Pyramid?

Volume = 1/3(a²)h

What is the Volume of a Triangular Prism?

Volume = 1/2(a)(b)(h)

What is the Volume of a Rectangular Prism?

Volume = lbh

Space inside Greenhouse 1 = volume of rectangular prism + volume of square pyramid = lbh + 1/3(a²)h

= (12)(12)(10)  + 1/3(12)(12)8

= 1,824 m³

Space inside Greenhouse 2 = volume of rectangular prism + volume of triangular prism = lbh + 1/2(a)(b)(h)

= (12)(12)(10) + 1/2(12)(8)(12)

= 2,016 m³

Space inside Greenhouse 2 - Greenhouse 1 = 192 m³

The true statements are B and E.

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