Solving a Hard Math Question: Volume of Concentrated Orange Juice

  • Thread starter DB
  • Start date
  • Tags
    Hard
In summary, the conversation discusses the question about finding the number of glasses that can be filled up to 1 cm from the rim when preparing orange juice from concentrate. The volume of the concentrate is represented by the expression (8x^3-54x+54)\picm^3 and 3 cans of water with the same volume are added to it. The glasses used have a height of 9 cm and a radius of (2x-3) cm. The simplified algebraic expression for the number of glasses is 4*(8x^3-54x+54)/(9*(2x-3)^2-1). The conversation also mentions the confusion caused by the wording of the question.
  • #1
DB
501
0
in my opinion, i find this question really hard.

-the volume of a can of concentrated orange juice is represented by the following expression:
[tex](8x^3-54x+54)\pi[/tex]cm^3
the juice is prepared by emptying the concentrate into a large container and by adding 3 cans of the same volume of water. after a good stir, the juice is poured into glasses measuring 9 cm in height and whose radius is (2x-3) cm. Use a simplified algebraic expression to represent the number of glasses that can be filled up to 1 cm from the rim.

i've drawn my diagrams i just don't know where to start. any help would be apreciated...
thanks in advance
 
Physics news on Phys.org
  • #2
The volume of the large container is 4*volume of oj concentrate

you would then divide that by the volume of the glass (-1 cm of height)
 
  • #3
o i see wat the question ment when it said "3 cans of water of the same volume" AS THE CONCENTRATE, its really badly written... thanks tho
 
  • #4
btw, you won't find a constant number, you will find a function of x
 

1. How do I find the volume of concentrated orange juice?

To find the volume of concentrated orange juice, you will need to know the density and mass of the juice. The formula for volume is volume = mass/density. Once you have these values, you can plug them into the formula to calculate the volume.

2. What is the formula for calculating volume?

The formula for calculating volume depends on the shape of the object. For a liquid, the formula is volume = mass/density. For a cube, the formula is volume = length x width x height. For a cylinder, the formula is volume = π x radius² x height. It is important to identify the shape of the object before using the appropriate formula to calculate volume.

3. Can I use any units to measure the volume of concentrated orange juice?

Yes, you can use any units to measure the volume of concentrated orange juice as long as they are consistent. For example, you can use milliliters (mL), liters (L), or cubic centimeters (cm³).

4. What is the density of concentrated orange juice?

The density of concentrated orange juice can vary depending on the brand and concentration level. Generally, it ranges from 1.1 to 1.2 grams per milliliter (g/mL). It is important to check the label or manufacturer's information for the specific density of the orange juice you are using.

5. Can I use the same formula to calculate the volume of any liquid?

Yes, the formula for calculating volume of a liquid is universal and can be used for any liquid. However, keep in mind that the density of different liquids may vary, so make sure to use the correct density for the specific liquid you are calculating the volume of.

Similar threads

  • Biology and Chemistry Homework Help
Replies
1
Views
3K
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
6K
  • Precalculus Mathematics Homework Help
Replies
5
Views
2K
  • Precalculus Mathematics Homework Help
Replies
12
Views
10K
  • Introductory Physics Homework Help
Replies
11
Views
3K
  • STEM Academic Advising
Replies
10
Views
4K
  • Calculus and Beyond Homework Help
Replies
22
Views
18K
  • General Discussion
3
Replies
78
Views
9K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
7
Views
2K
Back
Top