Question

The pyramid has the same base as the prism, and its height is 3 times the height of the prism. What is the ratio of the volume of the pyramid to the volume of the prism? a.volume of pyramid/volume of prism=1/9. b.volume of pyramid/volume of prism=1. c.volume of pyramid/volume of prism=3. d.volume of pyramid/volume of prism=2/3

Answer 1

Answer with Step-by-step explanation:

Volume of a prism = (Area of base) ×Height

Volume of a pyramid =
`(1)/(3)* (Area\ of\ base)* Height`

The pyramid has the same base as the prism.Hence, area of base will be same for both.Let it be a.

Height of pyramid is 3 times height of prism.

Let height of prism be h.

Height of pyramid=3h

Volume of a prism = ah

Volume of a pyramid =
`(1)/(3)* a* 3h`

= ah

Hence, Volume of pyramid/Volume of prism=1

Hence, correct option is:

b. volume of pyramid/volume of prism=1

Answer 2

the volume of the pyramid with a square base is equal to 1/3 s^2 h1 where s is the length of the side and h1 is the height. the volume of the prism is s^2 h2. since h1 is 3 times h2, the volume of the pyramid and that of the prism are equal. this is because the 1/3 constant cancels the 3 times enlargement of height