flat roof that is 22�Œ by 36�Œ
cylindrical cistern 12�Œ high and 5�Œ in diameter
Rain falls on a flat roof that is 22�Œ by 36�Œ. The rain drains into a cylindrical cistern 12�Œ high and 5�Œ in diameter. Assume that all of the rain drains into the cylinder (no evaporation or leaks.)
A. How many inches of rainfall will it take to fill the cistern to a depth of 4�Œ6��?
1. Formulas need:
2. Explain how you would approach solving this problem.
3. Show all work needed to find the solution.
B. How many more inches of rain on the roof would cause the cistern to overflow?
1. Formulas need:
2. Explain how you would approach solving this problem.
3. Show all work needed to find the solution.
A. To calculate how many inches of rainfall it will take to fill the cistern to a depth of 4¾ inches, we can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
First, we need to find the radius of the cylinder. The diameter is given as 5 inches, so the radius is half of that, which is 2.5 inches.
Next, we need to find the volume of the cylinder when it is filled to the desired depth. The height is given as 12 inches, but we only need to fill it to a depth of 4¾ inches, so the height will be 4¾ inches.
Using these values, we can plug them into the formula to find the volume:
Volume = π * (2.5)^2 * 4.75
Calculating this expression will give us the volume of the rainfall needed to fill the cistern to a depth of 4¾ inches.
B. To calculate how many more inches of rain on the roof would cause the cistern to overflow, we need to consider the maximum volume that the cistern can hold.
Again, we can use the formula for the volume of a cylinder, but this time we want to calculate the maximum volume of the cistern:
Volume = π * radius^2 * height
Using the same radius of 2.5 inches and height of 12 inches, we can find the maximum volume the cistern can hold.
Now, we need to subtract the current volume of water in the cistern from the maximum volume to find out how much more water it can hold. The current volume is the previous answer calculated in part A.
By subtracting the current volume from the maximum volume, we will obtain the amount of additional rainwater needed to cause the cistern to overflow.