Half of a sphere is stacked on top of a cone. They both share a circular base. The radius of the circle is 6 millimeters. The height of the cone is 14 millimeters. What is the volume of the composite figure? Express the answer in terms of π.

312π mm^2

Step-by-step explanation:

to find the volume of the figure, you have to calculate the volume of a cone and the volume of a sphere divided it by 2.

The volume of a cone is 1/3 * π * r ^ 2 * h, replacing the information:

V = 1/3 * (6) ^ 2 * (14) = 168π mm^2

The volume of a sphere is 4/3 * π * r ^ 3, replacing the information:

V = 4/3 * π * (6) ^ 3 = 288π mm^2

but since you only have half the sphere

V = 288π / 2 = 144π mm^2

then the total volume is

Vt = 168π + 144π = 312π mm^2

C. 312π mm3