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 4 inches, and the height of the cone is 6 inches. if the diameter of the bubble gum is 0.8 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 ) ( 4 ^ { 2 } ) ( 6 ) - \frac { 4 } { 3 } ( 3.14 ) ( 0.8 ^ { 3 } ) \\)
\\( \frac { 1 } { 3 } ( 3.14 ) ( 6 ^ { 2 } ) ( 4 ) - \frac { 4 } { 3 } ( 3.14 ) ( 0.8 ^ { 3 } ) \\)
\\( \frac { 1 } { 3 } ( 3.14 ) ( 4 ^ { 2 } ) ( 6 ) - \frac { 4 } { 3 } ( 3.14 ) ( 0.4 ^ { 3 } ) \\)
\\( \frac { 1 } { 3 } ( 3.14 ) ( 6 ^ { 2 } ) ( 4 ) - \frac { 4 } { 3 } ( 3.14 ) ( 0.4 ^ { 3 } ) \\)

Explanation:

Step1: Recall the volume formulas

The volume formula for a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\), and the volume formula for a sphere is \(V_{sphere}=\frac{4}{3}\pi r^{3}\).

Step2: Identify the values of \(r\) and \(h\) for the cone and sphere

For the cone, \(r = 4\) inches and \(h=6\) inches. For the sphere (bubble gum), \(d = 0.8\) inches, so \(r=\frac{d}{2}=0.4\) inches.

Step3: Substitute into the formula \(V = V_{cone}-V_{sphere}\)

Substitute \(r = 4\), \(h = 6\) into \(V_{cone}=\frac{1}{3}\pi r^{2}h\) and \(r = 0.4\) into \(V_{sphere}=\frac{4}{3}\pi r^{3}\). We get \(V=\frac{1}{3}(3.14)(4^{2})(6)-\frac{4}{3}(3.14)(0.4^{3})\)

Answer:

\(\frac{1}{3}(3.14)(4^{2})(6)-\frac{4}{3}(3.14)(0.4^{3})\) (the third option)