Question

Select the correct answer. A figure shows a pyramid of height 3 h and a rectangular prism of height h. This pyramid has the same base as the prism, and its height is three 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 B. volume of pyramid volume of prism = 1 9 C. volume of pyramid volume of prism = 3 D. volume of pyramid volume of prism = 2 3 Reset Next

Answer 1

Explanation:

The ratio of the volume of the pyramid to the volume of the prism is 1.so, the option A. is correct.

Let the base of the base of a prism is b and the height of the prism is h.

so, the volume of the prism-

V=
`b^(2)` h

also, given that base of the given pyramid is also b and the height of the pyramid is three times the height of the prism.

h'=3h

so, the volume of the square pyramid-

V'=
`(1)/(3)`
`b^(2)`h'

V'=
`(1)/(3)`
`b^(2)`(3h)

V'=
`b^(2)`h

so, now-

`(V')/(V)`=
`(b^(2)h )/(b^(2)h )`

`(V')/(V)`= 1

so. the ratio of the volume of the pyramid to the volume of the prism is 1.