Two similar cylinders contain juice.

Question

The first cylinder has radius 6 in and height 10 in., contains orange juice, and sells for $2.40. If grapefruit juice costs two-thirds of the price of an equal volume of orange juice, what is the cost of a container of grapefruit juice that has radius 9 in and height 15 in.

Answer 1

First, let's talk about proportions of the cylinders. 9:6=15:10=1.5

 

That means that cylinders are similar and the volume of the larger cylinder 1.5^3 times more than the volume of the smaller one. If we were to have an orange juice in that, it would cost 2.40 * (1.5)^3. But we have a grapefruit juice and it cost 2/3 of the orange juice.

 

So, we need to calculate (2/3)*2.40 * (1.5)^3.

 

Could you do that?

 

Let me know if you need more help with that.

 

Also, I'm available for online tutoring. 

Answer 2

Cost of Grapefruit = (2/3) * Cost of Orange Juice.

 

First, let's find the volume of the first cylinder. The volume of any cylinder is r² * h * π. So the volume here is 36 * 10 * π = 360π in³. Now we need to find the cost of orange juice per in³. To do that we'll divide $2.40 by the volume of the cylinder: $2.40/(360π in³). Let's plug this result into our first equation: Cost of Grapefruit = (2/3) * $2.40/(360π in³) = $1.6/(360π in³).

 

Yay! Now we know the Cost of Grapefruit. So let's just find the volume of the second cylinder and multiply the volume by the cost. Volume of Cylinder 2 = 9² * 15 * π = 1215π in³. Multiplying the volume by the Cost of Grapefruit: 1215π in³ * $1.6/(360π in³) = $5.4.

 

Therefore, the price you're looking for is $5.40.