Answer:
The volume of the triangular prism is not equal to the volume of the cylinder.
Step-by-step explanation:
we know that
The cross-sectional areas of a right triangular prism and a right cylinder are congruent
That means-----> The area of the triangular base of triangular prism is equal to the area of the circular base of the cylinder
step 1
Find the volume of triangular prism
The volume of triangular prism is equal to
[tex]V=BH[/tex]
where
B is the area of the triangular base
H is the height of the prism
we have
[tex]H=6\ units[/tex]
substitute
[tex]Vp=B(6)[/tex]
[tex]Vp=6B\ units^3[/tex]
step 2
Find the volume of cylinder
The volume of the cylinder is equal to
[tex]V=BH[/tex]
where
B is the area of the circular base
H is the height of the cylinder
we have
[tex]H=4\ units[/tex]
substitute
[tex]Vc=B(4)[/tex]
[tex]Vc=4B\ units^3[/tex]
step 3
Compare the volumes
[tex]\frac{Vp}{Vc}=\frac{6B}{4B}[/tex]
simplify
[tex]\frac{Vp}{Vc}=\frac{3}{2}=1.5[/tex]
so
[tex]Vp=1.5Vc[/tex]
so
The volume of the prism is 1.5 times the volume of the cylinder
therefore
The volume of the triangular prism is not equal to the volume of the cylinder.
