Question

The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 5 units, and the right cylinder has a height of 5 units. Which conclusion can be made from the given information?
The volume of the prism is half the volume of the cylinder.
The volume of the prism is twice the volume of the cylinder.
The volume of the prism is equal to the volume of the cylinder.
The volume of the prism is not equal to the volume of the cylinder.

Answer 1

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.