Step-by-step explanation:
Formulas.
Square: [tex]V = L \times W \times H[/tex]
Square Pyramid: [tex]V = \frac13b^2h[/tex]
b = base.
Let's work on the square first.
Substitute the Length, Width, and Height of the square into the formula:
[tex]V=15 \times15\times15[/tex]
Solve:
[tex]V=15^{3} =3,375[/tex]
Let's work on the square pyramid.
Substitute 225 into the formula, and 9 (height):
[tex]V=\frac{1}{3}(15)^2(9)[/tex]
Solve:
[tex]V=\frac{1}{3}225(9)[/tex]
[tex]V=\frac{1}{3}(2025)[/tex]
[tex]V=675[/tex]
Add each volume:
[tex]3,375+675=4,050 ft^{3}[/tex]
The total volume of the figure is [tex]4,050 ft^{3}[/tex].
