Question

Which statement wether Shannon is correct ?

Answer 1

Option B A rectangular prism in which BA=30 and h=5 has a volume of 150 units³, therefore, Shannon is correct

Explanation:

step 1

Find the area of the base of the rectangular pyramid

The volume of the rectangular pyramid is equal to

`V=(1)/(3)BH`

where

B is the area of the base and H is the height of the pyramid

we have

`V=50\ units^(3)`

`H=5\ units`

substitute and solve for B

`50=(1)/(3)B(5)`

`B=30\ units^(2)`

step 2

Find the volume of the rectangular prism with the same base area and height than the rectangular pyramid

The volume of the rectangular prism is equal to

`V=BH`

where

B is the area of the base and H is the height of the pyramid

we have

`B=30\ units^(2)`

`H=5\ units`

substitute

`V=(30)(5)=150\ units^(3)`

step 3

Compare the volumes

Volume of the rectangular pyramid ------->
`50\ units^(3)`

Volume of the rectangular prism ------->
`150\ units^(3)`

therefore

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

Shannon is correct