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A right cylinder with radius 3 centimeters and height 10 centimeters has a right cone on top of it with the same base and height 5 centimeters. Find the volume of the solid. Round your answer to two decimal places.

User Reben
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To find the volume of the solid, we need to calculate the volumes of the cylinder and the cone separately and then add them together.

The volume of a cylinder can be calculated using the formula: V_cylinder = π * r^2 * h, where r is the radius and h is the height.

For the cylinder:
Radius (r) = 3 cm
Height (h) = 10 cm

V_cylinder = π * (3 cm)^2 * 10 cm
V_cylinder = 90π cm^3

The volume of a cone can be calculated using the formula: V_cone = (1/3) * π * r^2 * h, where r is the radius and h is the height.

For the cone:
Radius (r) = 3 cm
Height (h) = 5 cm

V_cone = (1/3) * π * (3 cm)^2 * 5 cm
V_cone = 15π cm^3

Now, we can find the total volume by adding the volume of the cylinder and the cone:

Total Volume = V_cylinder + V_cone
Total Volume = 90π cm^3 + 15π cm^3
Total Volume = 105π cm^3

To round the answer to two decimal places, we can approximate π as 3.14:

Total Volume ≈ 105 * 3.14 cm^3
Total Volume ≈ 329.7 cm^3

Therefore, the volume of the solid is approximately 329.7 cm^3.

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