Question

An ice cream store offers a bowl with one giant scoop or two

regular scoops of ice cream for $2.75. A giant scoop is a sphere with a diameter of 6 centimeters. A regular scoop is a
sphere with a diameter of 4 centimeters. Which is closest to
the greatest volume of ice cream that can be purchased for $2.75?

A 67 cm
B 113 cm
C 536
D 905 cm​

Answer 1

B

Explanation:

The volume of a sphere is given by

`V=(4)/(3)\pi r^3`

where r is the radius

For $2.75, we can get 1 large OR 2 small scoops.

Giant scoop has diameter 6, so radius is half of that, which is 3, hence the volume is:

`V=(4)/(3)\pi r^3\\V=(4)/(3)\pi (3)^3\\V=113.1`

Regular scoop's diameter is 4, hence radius is 2. So volume of 1 regular scoop is:

`V=(4)/(3)\pi r^3\\V=(4)/(3)\pi (2)^3\\V=33.51`

We can get 2 of those, so total volume is 33.51 + 33.51 = 67.02

Hence, the max volume for $2.75 is around 113, answer choice B.