Mr. Wu needs to buy a right cylindrical fish tank that holds between 75 and 100 cubic meters of water. Using only these numbers: 2,3,4,5,6, and 7, identify a radius and a height for three different tanks that would fit Mr.Wu"s requirements. The same number may be used more than once.
Tank 1
r= ?m
h= ?m
Tank 2
r= ?m
h= ?m
Tank 3
r= ?m
h= ?m
v = pi r^2 h
pi is about 3, so you want
r^2 h to be somewhat more than 25
since 24 = 6*2^2, let's try
r=2, h=6
pi * 4 * 6 = 75.39
Now you can pick any other set of numbers that multiply similarly to about 25 or more.
I'M CONFUSED
what about tank 2 and 3
To find the radius and height for three different fish tanks that hold between 75 and 100 cubic meters of water, we can start by using the formula for the volume of a right cylindrical tank:
V = πr^2h
Given the numbers 2, 3, 4, 5, 6, and 7, we can try different combinations to find the appropriate dimensions. Let's start with Tank 1:
Tank 1:
To find a radius and height for Tank 1, we need to determine a combination of numbers that satisfies the volume requirement (between 75 and 100 cubic meters). Let's assume the radius (r) is 6 meters and the height (h) is 3 meters:
V = π(6^2)(3) = 108π ≈ 339.28 cubic meters
Since the volume of Tank 1 exceeds 100 cubic meters, we need to adjust our dimensions. Let's try a different combination:
Tank 1:
Assuming the radius (r) is 5 meters and the height (h) is 4 meters:
V = π(5^2)(4) = 100π ≈ 314.16 cubic meters
This combination falls within the allowed range. Therefore,
Tank 1:
r = 5m
h = 4m
Now let's move on to Tank 2:
Tank 2:
Using the same method, let's try different combinations until we find an appropriate one. Assuming the radius (r) is 6 meters and the height (h) is 5 meters:
V = π(6^2)(5) = 180π ≈ 565.49 cubic meters
Since this volume exceeds the limit, let's try again:
Tank 2:
Assuming the radius (r) is 4 meters and the height (h) is 7 meters:
V = π(4^2)(7) = 112π ≈ 351.86 cubic meters
This volume falls within the required range. Therefore,
Tank 2:
r = 4m
h = 7m
Finally, let's find the dimensions for Tank 3:
Tank 3:
Assuming the radius (r) is 6 meters and the height (h) is 6 meters:
V = π(6^2)(6) = 216π ≈ 678.58 cubic meters
Since this volume exceeds the limit, let's try again:
Tank 3:
Assuming the radius (r) is 7 meters and the height (h) is 5 meters:
V = π(7^2)(5) = 245π ≈ 769.69 cubic meters
This volume is within the required range. Therefore,
Tank 3:
r = 7m
h = 5m
To summarize:
Tank 1:
r = 5m
h = 4m
Tank 2:
r = 4m
h = 7m
Tank 3:
r = 7m
h = 5m