A gasoline truck is a cylindrical tank(think "sideways" cylinder) that is 20 feet long and 6 feet in diameter. At the end of his work day, the driver measures the depth of gasoline in the tank at 18 inches. How many gallons of gas are in the tank?
the radius of the tank is 36" (3 ft)
looking a the tank in cross section
the width of the gasoline surface is the base of an isosceles triangle
the height is ... 36 - 18
the sides are ... 36
use the vertex angle to find the area of the sector of the circle
then find the area of the segment representing the gasoline
area times length of tank is the volume of gasoline
convert to gallons
To find the number of gallons of gas in the tank, we need to find the volume of the cylindrical tank and convert it to gallons. Here's how you can do it step by step:
1. Find the volume of the cylindrical tank using the formula for the volume of a cylinder: V = π * r^2 * h, where V is the volume, π is a constant approximately equal to 3.14159, r is the radius of the tank, and h is the height (or depth) of the gas in the tank.
2. Convert the height from inches to feet, since the other measurements are given in feet. There are 12 inches in a foot, so divide the height of 18 inches by 12 to get 1.5 feet.
3. Calculate the radius of the tank. The diameter is given as 6 feet, so the radius (r) is half of the diameter, which is 6 / 2 = 3 feet.
4. Plug the values of the radius (r = 3 feet) and height (h = 1.5 feet) into the volume formula: V = π * 3^2 * 1.5.
5. Calculate the volume of the tank using a calculator or by multiplying: V ≈ 3.14159 * 3^2 * 1.5.
6. The resulting volume will be in cubic feet. Since we want to convert it to gallons, we need to use conversion factors. There are 7.48 gallons in 1 cubic foot.
7. Multiply the volume in cubic feet by the conversion factor: V * 7.48.
8. Calculate the final value to find the number of gallons of gas in the tank.
By following these steps, you will be able to determine the number of gallons of gas in the tank.