Answer to Question #124941 in Geometry for Jonathan

Question

A snow cone is a tasty treat with flavored ice and a spherical bubble gum ball at the bottom, as shown below:

Snow cone with spherical bubble gum ball at the bottom

The radius of the cone is 1.75 inches, and its height is 3.5 inches. If the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice?

11.15 in3

11.22 in3

0.07 in3

33.67 in3

Answer 1

Solution

Volume of the cone is $\frac{1}{3}\cdot(\pi\cdot r^2) \cdot h = \frac{1}{3}\cdot\pi\cdot 1.75^2\cdot3.5 \approx 11.2246$ in3

Volume of the sphere is $\frac{4}{3}\cdot\pi\cdot r^3 = \frac{4}{3}\cdot\pi\cdot(\frac{0.5}{2})^3 \approx 0.0654$ in3

Volume of the cone without a sphere is $11.2246-0.0654 \approx 11.1592$ in3

Answer: 11.15 in3