Question

Find the volume of a square pyramid with a height of 15 m and base edges of 4 m.
Question content area bottom
Part 1
Vequals
  
enter your response here m cubed
​(Round to the nearest tenth as​ needed.)

Answer 1

The volume \( V \) of a square 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.

For a square pyramid, the area of the base \( B \) can be found using:

\[
B = \text{side}^2
\]

Given that the length of each edge of the base is \( 4 \, \text{m} \):

\[
B = 4^2 = 16 \, \text{m}^2
\]

The height \( h \) of the pyramid is given as \( 15 \, \text{m} \).

Now, substituting these values into the volume formula:

\[
V = \frac{1}{3} \times 16 \, \text{m}^2 \times 15 \, \text{m}
\]

Calculating this:

\[
V = \frac{1}{3} \times 240 \, \text{m}^3
\]
\[
V = 80 \, \text{m}^3
\]

So, the volume of the square pyramid is:

\[
\boxed{80.0} \, \text{m}^3
\]

(Rounded to the nearest tenth as requested.)