Question

Please Help!!!! A composite figure is formed by placing a half-sphere atop a cylinder. The half-sphere and the cylinder both have a radius of 3 centimeters. The height of the cylinder is 10 centimeters.What is the exact volume of the composite figure?

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Answer 1

Explanation:

To find the volume of the composite figure, we need to find the volumes of the half-sphere and the cylinder separately, and then add them together.

The volume of the half-sphere is given by the formula:

V_half_sphere = (2/3)πr^3

where r is the radius of the half-sphere. In this case, the radius is 3 cm, so we have:

V_half_sphere = (2/3)π(3)^3

V_half_sphere = (2/3)π(27)

V_half_sphere = 18π

The volume of the cylinder is given by the formula:

V_cylinder = πr^2h

where r is the radius of the base of the cylinder, h is the height of the cylinder. In this case, the radius is 3 cm and the height is 10 cm, so we have:

V_cylinder = π(3)^2(10)

V_cylinder = 90π

To find the volume of the composite figure, we add the volumes of the half-sphere and the cylinder:

V_composite = V_half_sphere + V_cylinder

V_composite = 18π + 90π

V_composite = 108π

Therefore, the exact volume of the composite figure is 108π cubic centimeters.