Every employee works 9 hours per day
1 answer:
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Answer: max capacity is 1625 gallons.
Diagram is shown below.
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Explanation:
We'll draw two horizontal number lines to help make a comparison or connection between percentages and tank capacity.
For the top number line, make 5 sections with the labels: 0%, 20%, 40%, 60%, 100%. The reason I'm picking 5 is because 40% = 40/100 = 2/5. So having 40% capacity means we're 2/5 full. That denominator 5 tells us how to subdivide each number line.
The bottom number line will also have 5 sections. We only know one label for this bottom portion right now. That label is 650. Place this directly under the "40%". This visually is one way to represent that 650 gallons is 40% filled. See the diagram below.
Cut the 650 in half to get 325. This corresponds to 40% cut in half to get 20%. Therefore, 325 will go under the 20%. Being 20% full means we have 325 gallons of water.
To figure out the 60% portion, we will multiply 325 by 3. This is because 3*20% = 60%, so 3*325 = 975. We'll write "975 gallons" under the "60%"
Then we have 1300 gallons under the 80% since 4*325 = 1300. Note how 4*20% = 80%, so that's where the '4' multiplier comes from.
Finally, we multiply 325 by 5 to get 1625 and that represents the full tank's capacity. Technically we could have just jumped to this directly without having to find the 60% or 80% capacity values, but it's good practice I think.
Again the diagram is shown below. The answer we're after is at the very bottom right corner. It's under the 100% to indicate the tank is completely full, or has reached max capacity.
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Here's a way to find the answer without a double number line. This method involves setting up a proportion.
(40% full)/(650 gallons) = (100% full)/(x gallons)
40/650 = 100/x
40x = 650*100
40x = 65000
x = 65000/40
x = 1625
We confirm that the tank's max capacity is 1625 gallons.
let's notice something, we have a circle with a radius of 12 and one 90° sector is cut off, so only three 90° sectors of the circle are left shaded, so namely the cone will be using 3/4 of that circle.
think of it as, this shaded area is some piece of paper, and you need to pull it upwards and have the cutoff edges meet, and when that happens, you'll end up with a cone-shaped paper cup, and pour in some punch.
now, once we have pulled up the center of the circle to make our paper cup, there will be a circular base, its diameter not going to be 24, it'll be less, but whatever that base is, we know that is going to have the same circumference as those in the shaded area. Well, what is the circumference of that shaded area?
well then, the circumference of that circle at the bottom will be 18π, so, what is the diameter of a circle with a circumferenc of 18π?