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 (
), in cubic feet, figure can be determined by this expression:
(1)
Where:
- Radius of the circle of the right cone, in feet.
- Height of the cone, in feet.
- Width of the cuboid, in feet.
- Height of the cuboid, in feet.
- Length of the cuboid, in feet.
If we know that
,
,
,
and
, then the volume of the composite figure is:
![V = \frac{1}{3}\cdot \pi \cdot (10\,ft)^{2}\cdot (10\,ft) + (20\,ft)\cdot (7\,ft)\cdot (18\,ft)](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Ccdot%20%5Cpi%20%5Ccdot%20%2810%5C%2Cft%29%5E%7B2%7D%5Ccdot%20%2810%5C%2Cft%29%20%2B%20%2820%5C%2Cft%29%5Ccdot%20%287%5C%2Cft%29%5Ccdot%20%2818%5C%2Cft%29)
![V = \left(\frac{1000\pi}{3} + 2520\right)\,ft^{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cleft%28%5Cfrac%7B1000%5Cpi%7D%7B3%7D%20%2B%202520%5Cright%29%5C%2Cft%5E%7B3%7D)
![V \approx 3567.198\,ft^{3}](https://tex.z-dn.net/?f=V%20%5Capprox%203567.198%5C%2Cft%5E%7B3%7D)
The volume of the composite figure is approximately 3567.198 cubic feet.