Question

Which statements are true about a rectangular pyramid with a height of 9 centimeters and a base with the dimensions of 4 centimeters by 6 centimeters? Select two options. The area of the base of the pyramid, B, is 8 centimeters squared. The area of the base of the pyramid, B, is 24 centimeters squared. A rectangular prism with the dimensions of 9 centimeters by 4 centimeters by 6 centimeters will have 3 times volume of this pyramid. A rectangular prism with the dimensions of 9 centimeters by 4 centimeters by 6 centimeters will have One-third of the volume of this pyramid. The volume of this pyramid is 216 centimeters squared.\

Answer 1

B. The area of the base of the pyramid, B, is 24 centimeters squared.

C. A rectangular prism with the dimensions of 9 centimeters by 4 centimeters by 6 centimeters will have 3 times volume of this pyramid.

Explanation:

Given a rectangular pyramid with:

Height=9 cm

Base Dimensions = 4 centimeters by 6 centimeters

Base Area B=4 X 6 =24 Square cm.

Therefore, Option B (The area of the base of the pyramid, B, is 24 centimeters squared) is correct.

Volume of a pyramid =
`(1)/(3) $ X Base Area X Height`

`=(1)/(3) X 24X9=72 cm^3`

Volume of a Prism with the dimensions of 9 centimeters by 4 centimeters by 6 centimeters

=Base Area X Height

=24 X 9

`=216 cm^3`

Now, 216/72=3

Therefore, A rectangular prism with the same dimensions will have 3 times volume of this pyramid

Therefore, Option C is correct.