Find the height of each right cylinder

In summary, to construct 8 concrete right cylinders for hurricane protection on windows with a 4 inch radius, the height of each cylinder can be determined by using the formula V=pi*r^2*h, where V is the volume, r is the radius, and h is the height. Each cylinder weighs 1200 pounds, and since concrete weighs 150 pounds per cubic foot, the volume can be calculated by converting 1200 pounds into cubic feet and using it in the formula. The resulting height would be 22.96 feet.
  • #1
Meadow Delorto
2
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Homework Statement


I have to construct 8 concrete right cylinders for hurricane protection on windows, but I need to know the height to fit the given criteria. Each has a 4 inch radius and each weighs 1200 pounds. Concrete weighs 150 pounds per cubic foot.

V= volume of right cylinder
r=radius
h= height of right cylinder

Homework Equations


V=pi*r^2*h

The Attempt at a Solution


V=pi*r^2*h
1200 lbs= pi*16*h
h=23.8732 inches (1’11.87”).

I just don’t know where the weight of concrete, 150 pounds per cubic foot, comes into play. Thank you very much.
 
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  • #2
:welcome:You need to work in feet, not inches, and the equation you are missing is ## W=\delta \, V ##, where ## \delta ## is the density in pounds per cubic foot. When you compute the volume, the radius ## r ## needs to be converted to "x" feet. The answer you get for height ## h ## will be in feet.
 
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  • #3
In your statement, you set V=1200 pounds. That is not right; ##V=\frac{weight}{density}##. The density is what give is 150 pounds per cubic foot.
 
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  • #4
Charles Link said:
:welcome:You need to work in feet, not inches, and the equation you are missing is ## W=\delta \, V ##, where ## \delta ## is the density in pounds per cubic foot. When you compute the volume, the radius ## r ## needs to be converted to "x" feet. The answer you get for height ## h ## will be in feet.
Would I be correct if I said it would have to be 22.96 feet?
 
  • #5
Meadow Delorto said:

Homework Statement


I have to construct 8 concrete right cylinders for hurricane protection on windows, but I need to know the height to fit the given criteria. Each has a 4 inch radius and each weighs 1200 pounds. Concrete weighs 150 pounds per cubic foot.

V= volume of right cylinder
r=radius
h= height of right cylinder

Homework Equations


V=pi*r^2*h

The Attempt at a Solution


V=pi*r^2*h
1200 lbs= pi*16*h
h=23.8732 inches (1’11.87”).

I just don’t know where the weight of concrete, 150 pounds per cubic foot, comes into play. Thank you very much.

If the final object weighs 1200 lb and concrete weighs 150 lb/cu.ft., how many cubic feet of concrete does the object consist of? So, what is the object's volume, in cubic feet?
 
Last edited:
  • #6
You have the volume formula, and you know how much concrete and you have the density. So?

Convert 1200 pounds into the quantity in cubic feet.
Now use your volume formula to calculate the unknown height.
 

What is the formula for finding the height of a right cylinder?

The formula for finding the height of a right cylinder is h = V/πr^2, where h is the height, V is the volume, and r is the radius of the cylinder.

Can you find the height of a right cylinder without knowing its volume?

No, the height of a right cylinder cannot be determined without knowing its volume or at least one of its other dimensions (radius or area).

How do you find the height of a right cylinder if the radius is not given?

If the radius is not given, you can find the height of a right cylinder by using the formula h = V/πr^2 and solving for r. Once you have the radius, you can then use the formula to find the height.

Do all right cylinders have the same height?

No, the height of a right cylinder can vary depending on its dimensions. Two right cylinders can have the same volume but different heights if their radii are different.

Can you use the formula for finding the height of a right cylinder for other types of cylinders?

No, the formula h = V/πr^2 is specifically for right cylinders, which have a circular base and perpendicular sides. Other types of cylinders, such as oblique or elliptical cylinders, have different formulas for finding their height.

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