Question

question 3 (multiple choice worth 1 points) (06.01 mc) the cross - sectional areas of a triangular prism and a right cylinder are congruent. the triangular prism has a height of 10 units, and the right cylinder has a height of 7 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 not equal to 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.

Explanation:

Step1: Recall Volume Formulas

The volume of a prism (including triangular prism) is given by \( V_{prism} = B \times h_{prism} \), where \( B \) is the cross - sectional area and \( h_{prism} \) is the height of the prism. The volume of a cylinder is given by \( V_{cylinder}=B\times h_{cylinder} \), where \( B \) is the cross - sectional area (area of the base, which is a circle for a right cylinder) and \( h_{cylinder} \) is the height of the cylinder. In this problem, the cross - sectional areas of the triangular prism and the right cylinder are congruent, so we can denote the cross - sectional area as \( B \) for both.

Step2: Substitute the Given Heights

We know that the height of the triangular prism \( h_{prism} = 10 \) units and the height of the cylinder \( h_{cylinder}=7 \) units.
For the prism: \( V_{prism}=B\times10 = 10B \)
For the cylinder: \( V_{cylinder}=B\times7=7B \)

Step3: Compare the Volumes

Now we compare \( V_{prism} \) and \( V_{cylinder} \). Since \( 10B>7B \) (because \( B>0 \), as it represents an area), the volume of the prism is not equal to the volume of the cylinder. Also, \( 10B
eq\frac{1}{2}\times7B = 3.5B \) and \( 10B
eq3\times7B = 21B \) and \( 10B
eq7B \). So the volume of the prism is not equal to the volume of the cylinder.

Answer:

The volume of the prism is not equal to the volume of the cylinder.