Question

Find the total volume of the composite figure below. Round to the nearest thousandth.

Use the π key.

Answer 1

The volume of the composite figure is approximately 3567.198 cubic feet.

Explanation:

The composite figure consists in the combination of a right cone and a cuboid. The volume of the composite (
`V`), in cubic feet, figure can be determined by this expression:

`V = (1)/(3)\cdot \pi \cdot r^(2)\cdot h + w\cdot H \cdot l` (1)

Where:

`r` - Radius of the circle of the right cone, in feet.

`h` - Height of the cone, in feet.

`w` - Width of the cuboid, in feet.

`H` - Height of the cuboid, in feet.

`l` - Length of the cuboid, in feet.

If we know that
`r = 10\,ft`,
`h = 10\,ft`,
`w = 20\,ft`,
`H = 7\,ft` and
`l = 18\,ft`, then the volume of the composite figure is:

`V = (1)/(3)\cdot \pi \cdot (10\,ft)^(2)\cdot (10\,ft) + (20\,ft)\cdot (7\,ft)\cdot (18\,ft)`

`V = \left((1000\pi)/(3) + 2520\right)\,ft^(3)`

`V \approx 3567.198\,ft^(3)`

The volume of the composite figure is approximately 3567.198 cubic feet.