Answer:
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct
Step-by-step explanation:
step 1
Find the area of the base of the rectangular pyramid
we know that
The volume of the rectangular pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the base
H is the height of the pyramid
we have
[tex]V=40\ units^{3}[/tex]
[tex]H=6\ units[/tex]
substitute and solve for B
[tex]40=\frac{1}{3}B(6)[/tex]
[tex]120=B(6)[/tex]
[tex]B=120/6=20\ units^{2}[/tex]
step 2
Find the volume of the rectangular prism with the same base area and height
we know that
The volume of the rectangular prism is equal to
[tex]V=BH[/tex]
we have
[tex]B=20\ units^{2}[/tex]
[tex]H=6\ units[/tex]
substitute
[tex]V=(20)(6)=120\ units^{3}[/tex]
therefore
The rectangular prism has a volume that is three times the size of the given rectangular pyramid. Shannon is correct
