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? Select three options.

Answer 1

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:

The statements that are true about a rectangular pyramid

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:

The area of the base of the pyramid, B

The area of the base of the pyramid is equal to

`B=(12)(9)=108\ in^(2)`----------------------(1)

The volume of the pyramid

Substituting the values

`V=(1)/(3)(108)(15)=540\ in^(3)`------------------------(2)

The volume of the rectangular prism

V=BH

Substituting the values

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

Now,

(1) From(1) ,The area of the base of the pyramid, B, is
`36 in^3` is false, because we have found the volume as
`108 in^3`

(2).From (2),The area of the base of the pyramid, B, is
`108 in^3` is true

(3) From (2) and (3) A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have the same volume as this pyramid is false

because
`540 in^3 \\eq 1620 in^3`

4. From(2) The volume of this pyramid is 540in 3 is true

5. From(2) and (3) A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have 3 times volume of this pyramid is true

`540 * 3 = 1620`