Use the image to answer the question.
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 .
First, we need to calculate the volume of the cylinder using the formula V = πr^2h, where r is the radius and h is the height.
Vcylinder = π(6^2)(11)
Vcylinder = π(36)(11)
Vcylinder = π(396)
Vcylinder = 396π
Next, we need to calculate the total volume of the composite figure, which includes 2 half-spheres and the cylinder.
Vtotal = 2(Vhemisphere) + Vcylinder
Vtotal = 2(904.78) + 396π
Vtotal = 1809.56 + 396π
Vtotal ≈ 3072.12 m3
Therefore, the total volume of the composite three-dimensional figure shown is approximately 3072.12 cubic meters.
(1 point)
Responses
1,300.78 m3
1,300.78 m cubed
2,148.22 m3
2,148.22 m cubed
1,112.02 m3
1,112.02 m cubed
2,279.64 m3
Using the given volume of both hemispheres as 904.78 m^3, let's calculate the volume of the composite figure.
Volume of the hemispheres = 2 * 904.78 m^3
Volume of the hemispheres = 1809.56 m^3
Volume of the cylinder = π * r^2 * h
Volume of the cylinder = π * 6^2 * 11
Volume of the cylinder = π * 36 * 11
Volume of the cylinder = 396π
Total volume of the composite figure = Volume of hemispheres + Volume of cylinder
Total volume = 1809.56 + 396π
Total volume ≈ 1809.56 + 3843.94
Total volume ≈ 4653.5 m^3
Therefore, the correct answer is not provided in the response options.
Are u sure
I apologize for the mistake in my previous calculation.
Let's correct the calculation:
Total Volume = 2*(Volume of Hemisphere) + Volume of Cylinder
Total Volume = 2*(904.78) + 396π
Total Volume = 1809.56 + 396π
Total Volume ≈ 1809.56 + 396(3.14159)
Total Volume ≈ 1809.56 + 1244.69
Total Volume ≈ 3054.25 m^3
Therefore, the closest option among the provided response options is:
2,279.64 m^3