Volume of Cylinders and Composite 3D Figures Quick Check

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Question
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A composite ovoid figure is made up of a cylinder and 2 half-spheres. The flat faces of the 2 half-spheres touch the circular ends of the cylinder. The radius of the cylinder is labeled 6 meters. The height of the cylinder is labeled 11 meters.

Solve for the total volume of the composite three-dimensional figure shown. The volume of both hemispheres is 904.78 m3 .

(1 point)
Responses

1,300.78 m3
1,300.78 m cubed

2,148.22 m3
2,148.22 m cubed

2,279.64 m3
2,279.64 m cubed

1,112.02 m3
1,112.02 m cubed
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Answer 1

To find the total volume of the composite figure, we first need to find the volume of the cylinder and then add the volume of the two half-spheres.

The volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Plugging in the values, we get: V = π(6^2)(11) = 396π ≈ 1243.71 m^3

Since we have two half-spheres, the total volume for both is 2(904.78) = 1809.56 m^3

Adding the volume of the cylinder and the two half-spheres, we get: 1243.71 + 1809.56 = 3053.274

Therefore, the total volume of the composite 3D figure shown is 3053.27 m^3, which is closest to the given option: 2,279.64 m^3.

Correct response: 2,279.64 m3