For this case we have that by definition, the volume of a pyramid is given by:
[tex]V = \frac {A_ {b} * h} {3}[/tex]
Where:
[tex]A_ {b}:[/tex] It is the area of the base
h: It is the height
We have that the base is square, so the area is:
[tex]A_ {b} = 18 * 21 = 378 \ ft ^ 2[/tex]
On the other hand, we can find the height by the Pythagorean theorem:
[tex]h = \sqrt {41 ^ 2 - (\frac {18} {2}) ^ 2}\\h = \sqrt {41 ^ 2- (9) ^ 2}\\h = \sqrt {1681-81}\\h = \sqrt {1600}\\h = 40 \ ft[/tex]
Finally, the volume is:
[tex]V = \frac {378 * 40} {3}\\V = 5040 \ ft ^ 3[/tex]
Answer:
Option B
