A liquid shake is being served in a cone shaped container with a base diameter of 8 centimeters and a height of 22 centimeters. The shake has a density of 0.82 grams per cubic centimeter and fills the entire cone. If the total weight of the container and shake is 330 grams, which of the following is the weight of the container? *

19 grams

23 grams

28 grams

31 grams

The container weighs approximately 28 g.

Step-by-step explanation:

In order to solve this problem we first need to calculate the volume of the container, since it's shaped like a cone we must use the following formula:

volume container = (pi*r²*h) / 3

Applying the data from the problem:

r = d / 2 = 8/2 = 4 cm

volume container = [pi * (4) ²*22]/3

volume container = (pi*16*22) / 3

volume container = (352*pi) / 3 = 368.6135 cm³

Since the density is 0.82 g/cm³, we can find the mass of the shake by using the following formula:

density = mass / volume

shake mass = density*volume = 0.82*368.6135 = 302.26307 g

Since the container plus shake weighs 330 grams, then the container alone weighs:

container = 330 - 302.26307 = 27.73693 g

The container weighs approximately 28 g.