Question

The figure shows a right circular cone on top of a half-sphere with the same radius. If the cone has a radius of 2 cm and height of 6 cm, what is the approximate volume of this solid? Note: The volume of a cone is given by V = 1/3r2h and the volume of a sphere is given by V = 4/3r3. A. 59 cm3 B. 176 cm3 C. 42 cm3 D. 109 cm3

Answer 1

First find the volume of cone then the hemisphere and add them together.

V of cone = 1/3πr²h
V of cone = 1/3(3.14)(2)²(6)
V of cone = 25.12 cm³

V of hemisphere = 2/3πr³
V of hemisphere = 2/3(3.14)(2)³
V of hemisphere = 16.75 cm³

Volume of the whole figure = 25.12 + 16.75 = 41.87 cm²

Due to the answer choices it is closest to C. 42 cm³