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.

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BrownnBarbiee BrownnBarbiee

09-05-2019
Mathematics

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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.

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calculista calculista · Answer 1 · 2019-05-19T19:57:00+02:00

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 pyramid

Step-by-step explanation:

step 1

Find the volume of the rectangular prism

The volume is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

Find the area of the base B

[tex]B=5^{2}=25\ in^{2}[/tex]

substitute

[tex]Vprism=25h\ in^{3}[/tex]

step 2

Find the volume of the square pyramid

The volume is equal to

[tex]V=(1/3)Bh[/tex]

where

B is the area of the base

h is the height of the pyramid

Find 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 prism

or

[tex]Vprism=3Vpyramid[/tex]

The volume of the prism is three times the volume of the pyramid