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 nestled at the bottom of the cone. the radius of the snow cone is 4 inches, and the height of the cone is 8 inches. if the diameter of the bubble gum is 0.6 inches, which of the following can be used to calculate the volume of the cone that can be filled with flavored ice?
options with volume formulas
question 18
abcd is a quadrilateral inscribed in a circle, as shown below:
image of cyclic quadrilateral with angle labels
what equation can be used to solve for angle c?
options with angle equations

Explanation:

First Problem (Snow Cone Volume)

Step1: Volume of the cone

The formula for the volume of a cone is $V_{cone}=\frac{1}{3}\pi r^2 h$. Here, $r=4$, $h=6$, using $\pi\approx3.14$:
$V_{cone}=\frac{1}{3}(3.14)(4)^2(6)$

Step2: Volume of the bubble gum

The diameter of the sphere is 0.8, so radius $r=0.4$. The volume of a sphere is $V_{sphere}=\frac{4}{3}\pi r^3$:
$V_{sphere}=\frac{4}{3}(3.14)(0.4)^3$

Step3: Subtract sphere from cone

The fillable volume is $V_{cone}-V_{sphere}$:
$\frac{1}{3}(3.14)(4)^2(6)-\frac{4}{3}(3.14)(0.4)^3$

Step1: Recall cyclic quadrilateral property

In a cyclic quadrilateral, opposite angles sum to $180^\circ$. Angle A $(x+15)^\circ$ is opposite angle C $(2x+15)^\circ$, so their sum equals $180^\circ$.

Step2: Set up the equation

$(x+15)+(2x+15)=180$

Answer:

$\boldsymbol{\frac{1}{3}(3.14)(4)^2(6)-\frac{4}{3}(3.14)(0.4)^3}$ (matches the first option)

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Second Problem (Inscribed Quadrilateral)