Question

The cross-sectional areas of a right triangular prism and a right cylinder are congruent. The right triangular prism has a height of 6 units, and the right cylinder has a height of 6 units. Which conclusion can be made from the given information? The volume of the triangular prism is half the volume of the cylinder. The volume of the triangular prism is twice the volume of the cylinder. The volume of the triangular prism is equal to the volume of the cylinder. The volume of the triangular prism is not equal to the volume of the cylinder.

Answer 1

the answer is C for short

Answer 2

The correct answer is:

The volume of the triangular prism is equal to the volume of the cylinder

Explanation:

Given that there are two figures

1. A right triangular prism and

2. Right cylinder

Area of cross section of prism is equal to Area of cross section of cylinder.

Let this value be A.

Also given that Height of prism = Height of cylinder = 6

Volume of a prism is given as:

`V_(Prism) = \text{Area of cross section} * Height`

`V_(Prism) = A * 6 ........ (1)`

Cross section of cylinder is a circle.

Area of circle is given as:
`\pi r^(2)`

Area of cross section, A =
`\pi r^(2)`

Volume of cylinder is given as:

`V_(Cylinder) = \pi r^(2) h\\\Rightarrow V_(Cylinder) = A * h\\\Rightarrow V_(Cylinder) = A * 6 ...... (2)`

From equations (1) and (2) we can see that

`V_(Prism)=V_(Cylinder)`

Hence, the correct answer is:

Volume of prism is equal to the volume of cylinder.