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pochemuha
3 years ago
11

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

Mathematics
1 answer:
cestrela7 [59]3 years ago
3 0

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 (V), in cubic feet, figure can be determined by this expression:

V = \frac{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 = \frac{1}{3}\cdot \pi \cdot (10\,ft)^{2}\cdot (10\,ft) + (20\,ft)\cdot (7\,ft)\cdot (18\,ft)

V = \left(\frac{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.

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