Question

snowys snow cones has a special bubble gum snow cone on sale. the cone is a regular snow cone that has a spherical piece of bubble gum nested at the bottom of the cone. the radius of the snow cone is 2 inches, and the height of the cone is 3 inches. if the diameter of the bubble gum is 0.5 inches, which of the following can be used to calculate the volume of the cone that can be filled with flavored ice?
$\frac{1}{3}(3.14)(2^{2})(3)-\frac{4}{3}(3.14)(0.25^{3})$
$\frac{1}{3}(3.14)(3^{2})(2)-\frac{4}{3}(3.14)(0.25^{3})$
$\frac{1}{3}(3.14)(2^{2})(3)-\frac{4}{3}(3.14)(0.5^{3})$
$\frac{1}{3}(3.14)(3^{2})(2)-\frac{4}{3}(3.14)(0.5^{3})

Explanation:

Step1: Find volume formula for cone

The volume formula for a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$, where $r = 2$ inches (radius of cone) and $h = 3$ inches (height of cone), so $V_{cone}=\frac{1}{3}(3.14)(2^{2})(3)$.

Step2: Find volume formula for sphere

The volume formula for a sphere is $V_{sphere}=\frac{4}{3}\pi r^{3}$. The diameter of the bubble - gum sphere is $0.5$ inches, so the radius $r = 0.25$ inches. Then $V_{sphere}=\frac{4}{3}(3.14)(0.25^{3})$.

Step3: Calculate volume for flavored ice

The volume of the cone that can be filled with flavored ice is the volume of the cone minus the volume of the sphere, which is $\frac{1}{3}(3.14)(2^{2})(3)-\frac{4}{3}(3.14)(0.25^{3})$.

Answer:

$\frac{1}{3}(3.14)(2^{2})(3)-\frac{4}{3}(3.14)(0.25^{3})$