Question

Kristen gets a full scoop of frozen yogurt in a cone. The scoop is aperfect sphere with the same radius as the cone. She wonders if theentire volume of the frozen yogurt could fit completely inside thecone. What is the relationship between the volume of the coneand the volume of frozen yogurt? Is the volume of the cone greatenough to fit all of the frozen yogurt? Explain. (Use 3.14 for (pie) andround your answer to the nearest whole number)

Answer 1

The volume of a sphere is calculated as follows:

$V=\frac{4}{3}\pi r^3$

where r is the radius of the sphere.

Substituting with r = 5 cm, we get:

$\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot5^3 \\ V=\frac{4}{3}\cdot\pi\cdot125 \\ V=523.3\operatorname{cm}^3 \end{gathered}$

The volume of a right circular cone is calculated as follows:

$V=\pi r^2\frac{h}{3}$

where h is the height of the cone.

Substituting with r = 5 cm, and h = 11 cm, we get:

$\begin{gathered} V=\pi\cdot5^2\cdot\frac{11}{3} \\ V=\pi\cdot25\cdot\frac{11}{3} \\ V=287.8\operatorname{cm}^3 \end{gathered}$

The volume of the cone is less than the volume of the sphere, then the

entire volume of the frozen yogurt cannot fit completely inside the

cone.