Metal discs for pet collars have a diameter of 4cm. Each disc is 0.1cm thick. How many discs can be made from 1000cm3 of metal?
I don't like this question.
There is simple purely mathematical solution
volume of 1 disc = π(2^2)(.1) = .4π cm^3
so number of discs = 1000/(.4π) or 795.8
so they can make 795 discs
Logistically, this is a very ambiguous question
- is the 1000 cm^3 in a block of metal or in sheets?
- are the discs manufactured by pouring liquid metal into a mould ?
- are they stamped ? If so, is the scrap metal used again?
- arhhh! ....
To find out how many discs can be made from 1000cm³ of metal, we first need to find the volume of a single disc.
The volume of a disc can be calculated using the formula:
Volume = π * (radius)² * height
In this case, the diameter of each disc is given as 4cm, so the radius is half of that, which is 2cm. The height (thickness) of each disc is given as 0.1cm.
Plugging these values into the formula, we get:
Volume = π * (2cm)² * 0.1cm
Volume = π * 4cm² * 0.1cm
Volume = π * 16cm² * 0.1cm
Volume = 1.6π cm³
Now we know that the volume of each disc is 1.6π cm³.
To find out how many discs can be made from 1000cm³ of metal, we need to divide the total volume of metal by the volume of each disc:
Number of discs = Total volume of metal / Volume of each disc
Number of discs = 1000cm³ / 1.6π cm³
Now, to calculate the exact number of discs, we need to evaluate the division:
Number of discs = 1000cm³ / 1.6π cm³ ≈ 1000 / 1.6π
Since we don't have an exact value for π, we can use the approximation 3.14:
Number of discs ≈ 1000 / (1.6 * 3.14)
Number of discs ≈ 1000 / 5.024
Number of discs ≈ 199.2
Therefore, approximately 199 discs can be made from 1000cm³ of metal.