Question

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.

144π mm3
168π mm3
312π mm3
456π mm3

Answer 1

Hemisphere: (1/2)*(4/3)πr^3 = (2/3)π(6^3) = (2/3)π(216) = 144π mm^3.
Cone: (1/3)πr^2h = (1/3)π(6^2)(14) = (1/3)π(36)(14) = 168π mm^3.
Total = 144π + 168π = 312π mm^3.

Answer: 312π mm^3.