#24. A cylindrical water well is 1,200 ft. deep and 6 in. across. Find the lateral surface area of the well. Round to the nearest square foot. (Hint: Convert measures to a common unit.)
A = 2πrh
A = 2 * 3.14 * 0.25 * 1200
To find the lateral surface area of the cylindrical water well, we need to use the formula for the lateral surface area of a cylinder, which is given by:
Lateral Surface Area = 2πrh,
where r is the radius of the base of the cylinder and h is the height of the cylinder.
First, we need to convert the measurements to a common unit. The height is given as 1,200 ft, and the diameter (6 in) represents the diameter of the base.
To convert the diameter to the radius, we divide it by 2:
Radius = Diameter/2 = 6 in/2 = 3 in.
Since the height is given in feet, we need to convert the radius from inches to feet:
3 in * (1 ft/12 in) = 0.25 ft.
Now we have the measurements in a common unit, so we can plug them into the formula:
Lateral Surface Area = 2πrh = 2π * 0.25 ft * 1,200 ft
Next, calculate the value:
Lateral Surface Area ≈ 2π * 0.25 ft * 1,200 ft ≈ 1,507.96 ft².
Therefore, the lateral surface area of the cylindrical water well is approximately 1,508 square feet, rounded to the nearest square foot.