Use the image to answer the question.

A triangular pyramid with a square base has a dotted line segment labeled h equals 8 meters extending from the top vertex to the base. The base of the pyramid is labeled a equals 60 meters squared.

Joao constructs a square-based pyramid. What is the volume of the pyramid?

(1 point)
The volume of the pyramid is
cubic meters.

1 answer

The volume \( V \) of a pyramid can be calculated using the formula:

\[ V = \frac{1}{3} \times B \times h \]

where \( B \) is the area of the base and \( h \) is the height of the pyramid.

From the information given:

  • The area of the base \( B = 60 \) square meters.
  • The height \( h = 8 \) meters.

Now we can substitute these values into the volume formula:

\[ V = \frac{1}{3} \times 60 \text{ m}^2 \times 8 \text{ m} \]

Calculating this gives:

\[ V = \frac{1}{3} \times 60 \times 8 = \frac{480}{3} = 160 \text{ m}^3 \]

Thus, the volume of the pyramid is

\[ \boxed{160} \text{ cubic meters}. \]