Question

1. what is the volume of this triangular pyramid?

4 cm
4 cm 3 cm

1. cubic centimeters

Explanation:

Step1: Recall the volume formula for a triangular pyramid (tetrahedron). The volume \( V \) of a pyramid is given by \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid.

For a triangular base, the area of the base \( B \) is calculated using the formula for the area of a triangle: \( B = \frac{1}{2} \times \text{base length of triangle} \times \text{height of triangle} \). From the diagram, the base of the triangular base is \( 4 \, \text{cm} \) and the height of the triangular base is \( 3 \, \text{cm} \). So, \( B=\frac{1}{2}\times4\times3 \).
Calculating \( B \): \( \frac{1}{2}\times4\times3 = 2\times3=6 \, \text{cm}^2 \).

Step2: Identify the height of the pyramid. The height of the pyramid (the perpendicular height from the apex to the base) is given as \( 4 \, \text{cm} \). Now, use the volume formula for the pyramid \( V = \frac{1}{3}Bh \). Substitute \( B = 6 \, \text{cm}^2 \) and \( h = 4 \, \text{cm} \) into the formula.

So, \( V=\frac{1}{3}\times6\times4 \).
First, calculate \( \frac{1}{3}\times6 = 2 \). Then, \( 2\times4 = 8 \).

Answer:

\( 8 \)