Question

Karen gets a full scoop of frizen yogurt in a cone.The scoop is a perfect sphere with the same radius as the cone.She wonders if the entire volume of the frozen yogurt could fit completly inside the cone. What is the relationship between the volume of the cone and the volume of the frozen yogurt ? Explain (use 3.14for pie and round your answers to the nearest whole number)

Answer 1

Answer:

In order to fit inside the cone, the volume of frozen yogurt (half sphere in shape) must be smaller than the volume of cone

Explanation:

Image for the question is attached as image

In order to fit inside the cone, the volume of frozen yogurt (half sphere in shape) must be smaller than the volume of cone

The volume of the cone as shown in the image is

$\frac{1}{3} \pi r^{2} h$

Substituting the values in above equation we get

$\frac{1}{3} * (3.14) * (\frac{5}{2})^2*11\\= 71.99$

The volume of the frozen yogurt (half sphere in shape)  as shown in the image is

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

Substituting the values in above equation we get

$\frac{4}{3} * (3.14) * (2.5)^3\\= 65.44$

Hence, the volume of frozen yoghurt is smaller than the volume of cone