Question

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?

Answer 1

Above Is Correct But Here's The Answer Choices For PLATO USERS

Answer:

`(VolumeOfPyramid)/(VolumOfPrism)=1`

Explanation:

`(1)/(3)*Base*Height`

`Base*Height`

Volume Of Prism =
`A*base`

Volume Of Pyramid =
`(1)/(3)*3A*Base=A*Base`

Going Back toe the Question its asking,"what is the ratio of the volume of the pyramid to the volume of the prism?"

`\left[\begin{array}{ccc}Answer&Choices\end{array}\right]`

`\left[\begin{array}{ccc}(VolumeOfPyramid)/(VolumOfPrism)=1&Correct\end{array}\right]`

`\left[\begin{array}{ccc}(VolumeOfPyramid)/(VolumOfPrism)=(1)/(9)\end{array}\right]`

`\left[\begin{array}{ccc}(VolumeOfPyramid)/(VolumOfPrism)=3\end{array}\right]`

`\left[\begin{array}{ccc}(VolumeOfPyramid)/(VolumOfPrism)=(2)/(3)\end{array}\right]`

Answer 2

the formula of the volume of pyramid =1/3*h*base
the volume of prism=base*h
we know that the height of pyramid is 3 times more than the height of prism so that if the height of prism is a ==> the volume of prism is a*base
the height of prism is 3a so that ==> the volume of pyramid is ==>1/3*3a*base=a*base
The Answer of the ratio is 1/1