A cylindrical storage tank has a height of 100 feet and a diameter of 10 feet.
(Use pi = 3.14)
What is the lateral surface area of the tank?
How do i find lateral surface area of the tank
What is the volume?
7850 cubic feet
What is the volume in gallons of water if 7.48 gallons= 1 cubic foot?
58718 gallons
To find the lateral surface area of the tank, you need to calculate the area of the side of the cylinder excluding the top and bottom surfaces.
The formula for the lateral surface area of a cylinder is given by:
Lateral Surface Area = 2 * π * r * h
Where:
π = 3.14 (approximation of pi)
r = radius of the cylinder (half of the diameter)
h = height of the cylinder
Given that the diameter of the tank is 10 feet, we can find the radius by dividing it by 2:
r = 10 ft / 2 = 5 ft
Using the height of the tank, which is given as 100 feet, and the radius, we can plug these values into the formula to find the lateral surface area:
Lateral Surface Area = 2 * 3.14 * 5 ft * 100 ft
Lateral Surface Area = 3140 ft²
Therefore, the lateral surface area of the tank is 3140 square feet.
To find the volume of the tank, you can use the formula for the volume of a cylinder:
Volume = π * r² * h
Using the given values, the radius and height of the tank are the same as before, so we can plug them into the formula:
Volume = 3.14 * (5 ft)² * 100 ft
Volume = 3.14 * 25 ft² * 100 ft
Volume = 78500 ft³
Therefore, the volume of the tank is 78500 cubic feet.
To convert the volume from cubic feet to gallons, we'll use the conversion factor given: 7.48 gallons = 1 cubic foot.
To find the volume in gallons, we need to multiply the volume in cubic feet by the conversion factor:
Volume (gallons) = Volume (cubic feet) * 7.48 gallons/ft³
Volume (gallons) = 78500 ft³ * 7.48 gallons/ft³
Volume (gallons) ≈ 58718 gallons
Therefore, the volume of the tank is approximately 58718 gallons.