Answer:
The volume of the composite figure is approximately 3567.198 cubic feet.
Step-by-step explanation:
The composite figure consists in the combination of a right cone and a cuboid. The volume of the composite ([tex]V[/tex]), in cubic feet, figure can be determined by this expression:
[tex]V = \frac{1}{3}\cdot \pi \cdot r^{2}\cdot h + w\cdot H \cdot l[/tex] (1)
Where:
[tex]r[/tex] - Radius of the circle of the right cone, in feet.
[tex]h[/tex] - Height of the cone, in feet.
[tex]w[/tex] - Width of the cuboid, in feet.
[tex]H[/tex] - Height of the cuboid, in feet.
[tex]l[/tex] - Length of the cuboid, in feet.
If we know that [tex]r = 10\,ft[/tex], [tex]h = 10\,ft[/tex], [tex]w = 20\,ft[/tex], [tex]H = 7\,ft[/tex] and [tex]l = 18\,ft[/tex], then the volume of the composite figure is:
[tex]V = \frac{1}{3}\cdot \pi \cdot (10\,ft)^{2}\cdot (10\,ft) + (20\,ft)\cdot (7\,ft)\cdot (18\,ft)[/tex]
[tex]V = \left(\frac{1000\pi}{3} + 2520\right)\,ft^{3}[/tex]
[tex]V \approx 3567.198\,ft^{3}[/tex]
The volume of the composite figure is approximately 3567.198 cubic feet.
