Question

Me. Jackson has an empty pyramid and an empty prism. The base of the pyramid is congruent to the base of the prism, and their heights are equal. Determine the number of times Mr. Jackson must fill the pyramid with water and pour it into the prism in order to completely fill the prism with water

Answer 1

Volume of water required to fill the pyramid is
`(1)/(3)`rd of the water required to fill the prism completely.

Explanation:

Let Mr Jackson has an empty rectangular pyramid and rectangular prism.

Height and base of both are congruent.

So volume of rectangular pyramid
`V_(1)=(1)/(3)(\text{Area of the base})(\text{Height})`

`V_(1)=(1)/(3)(A_(1))(h)`

Volume of the rectangular prism = (Area of the base)(height)

`V_(2)=(A_(2))(h)`

`(V_(1))/(V_(2))=((1)/(3)(A)h)/((A)h)` [ Since
`A_(1)= A_(2)` ]

`(V_(1))/(V_(2))=(1)/(3)`

`V_(1)=(1)/(3)(V_(2))`

Therefore, amount of water required to fill the pyramid is
`(1)/(3)`rd of the water required to fill the prism completely.