Answer:
C. The volume of the prism is equal to the volume of the cylinder
Step-by-step explanation:
Given
Congruent area of cylinder and triangular prism
Height of triangular prism = 5 units
Height of Cylinder = 5 units
Required
Relationship between the volumes of both shapes.
Let H₁ and H₂ represent the height of the cylinder and the triangular prism
H₁ = H₂ = 5 units
From the question, we have that both shapes have a congruent area.
This means that they have the same base area.
Let this be represented by A
So;
Calculating the volume of the cylinder
V₁ = Base Area (A) * Height (H₁)
V₁ = A * 5
V₁ = 5A
Calculating the volume of the triangular prism
V₂ = Base Area (A) * Height (H₂)
V₂ = A * 5
V₂ = 5A
Comparing both volumes.
V₁ = 5A
V₂ = 5A
Since V₁ = V₂ = 5A, then we can conclude that both shapes have the same volume.
