Question

Which statements are true about a rectangular pyramid with a height of 15 inches and a base with the dimensions of 12 inches and 9 inches? Check all that apply.

1.The area of the base of the pyramid, B, is 36 in3
2.The area of the base of the pyramid, B, is 108 in3
3.A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have the same volume as this pyramid.

4.The volume of this pyramid is 540in 3

5.A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have 3 times volume of this pyramid.

Answer 1

2,4,5

Explanation:

Answer 2

2.The area of the base of the pyramid, B, is 108 in3

4.The volume of this pyramid is 540in 3

5.A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have 3 times volume of this pyramid.

Explanation:

Verify each statement

Part 1) The area of the base of the pyramid, B, is 36 in3

The statement is false

Because

The area of the base of the pyramid is equal to

`B=(12)(9)=108\ in^(2)`

Part 2) The area of the base of the pyramid, B, is 108 in3

The statement is true

see the Part 1)

Part 3) A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have the same volume as this pyramid.

The statement is false

Because

The volume of the pyramid is equal to

`V=(1)/(3)BH`

substitute

`V=(1)/(3)(108)(15)=540\ in^(3)`

The volume of the rectangular prism is equal to

`V=BH`

substitute

`V=(108)(15)=1,620\ in^(3)`

Compare

`540\ in^(3)\\eq 1,620\ in^(3)`

Part 4) The volume of this pyramid is 540in 3

The statement is true

see the part 3)

Part 5) A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have 3 times volume of this pyramid.

The statement is true

Because

we have

Volume of the pyramid ------>
`540\ in^(3)`

Volume of the rectangular prism ----->
`1,620\ in^(3)`

Divide the volume of rectangular prism by the volume of the pyramid

`1,620\ in^(3)/540\ in^(3)=3`

therefore

The volume of the rectangular prism is 3 times greater than the volume of the pyramid