Question

Which statement wether Shannon is correct ?

Answer 1

Answer:

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

Step-by-step explanation:

step 1

Find the area of the base of the rectangular pyramid

The volume of the rectangular pyramid is equal to

$V=\frac{1}{3}BH$

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

$50=\frac{1}{3}B(5)$

$B=30\ units^{2}$

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