MATH SOLVE

2 months ago

Q:
# Explain the relationship between the volumes of a square pyramid and a rectangular prism if they each have a square bass with side length of 5 inches and they each have a height oh h inches.

Accepted Solution

A:

Answer:The volume of the pyramid is one third the volume of the rectangular prism or The volume of the prism is three times the volume of the pyramidStep-by-step explanation:step 1Find the volume of the rectangular prismThe volume is equal to[tex]V=Bh[/tex]whereB is the area of the baseh is the height of the prismFind the area of the base B[tex]B=5^{2}=25\ in^{2}[/tex]substitute[tex]Vprism=25h\ in^{3}[/tex]step 2Find the volume of the square pyramidThe volume is equal to[tex]V=(1/3)Bh[/tex]whereB is the area of the baseh is the height of the pyramidFind the area of the base B[tex]B=5^{2}=25\ in^{2}[/tex]substitute[tex]Vpyramid=(1/3)25h\ in^{3}[/tex]Remember that[tex]Vprism=25h\ in^{3}[/tex]substitute[tex]Vpyramid=(1/3)Vprism[/tex]The volume of the pyramid is one third the volume of the rectangular prismor[tex]Vprism=3Vpyramid[/tex]The volume of the prism is three times the volume of the pyramid