Question

the following triangular prism has a volume of 10 cubic units and a height of 5 units. the triangular pyramid has a congruent base and the same height, and its longest edge is 7.5 units long.

what is the volume of the pyramid?
choose 1 answer:
a (\frac{10}{3}) cubic units
b (\frac{15}{3}) cubic units
c 10 cubic units
d 15 cubic units

Explanation:

Step1: Recall the volume formulas

The volume of a prism is given by \( V_{\text{prism}} = B \times h \), where \( B \) is the area of the base and \( h \) is the height of the prism. The volume of a pyramid with the same base and height as the prism is given by \( V_{\text{pyramid}} = \frac{1}{3} \times B \times h \).

Step2: Relate the volumes

Since the triangular pyramid (which is a type of pyramid) has a congruent base and the same height as the triangular prism, we can see that the volume of the pyramid is \( \frac{1}{3} \) of the volume of the prism.

Step3: Calculate the volume of the pyramid

We know the volume of the prism is 10 cubic units. So, the volume of the pyramid is \( \frac{1}{3} \times 10=\frac{10}{3} \) cubic units.

Answer:

A. \(\frac{10}{3}\) cubic units