You are standing 14 feet from the edge of a cylindrical water tank and 26 feet from a point of tangency. The tank is 10 feet tall. What is the volume of the tank in cubic feet?
6.4
To find the volume of a cylindrical water tank, we need to know the radius of the tank. From the given information, we can see that we have a right triangle formed by the distance from the edge of the tank, the distance from the point of tangency, and the height of the tank.
Using the Pythagorean theorem, we can find the radius of the tank. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have:
(radius + distance from the edge)^2 = (distance from the point of tangency)^2 + (height of the tank)^2
Substituting the given values, we get:
(radius + 14)^2 = 26^2 + 10^2
Simplifying the equation:
(radius + 14)^2 = 676 + 100
(radius + 14)^2 = 776
Taking the square root of both sides:
radius + 14 = √776
radius + 14 ≈ 27.86
Subtracting 14 from both sides:
radius ≈ 27.86 - 14
radius ≈ 13.86
Now that we know the radius of the tank, we can calculate its volume. The formula for the volume of a cylinder is:
Volume = π * radius^2 * height
Substituting the values we have:
Volume = π * (13.86)^2 * 10
Using the approximation π ≈ 3.14:
Volume ≈ 3.14 * (13.86)^2 * 10
Volume ≈ 3.14 * (191.8596) * 10
Volume ≈ 3.14 * 1918.596
Volume ≈ 6027.2304 cubic feet
Therefore, the volume of the tank is approximately 6027.2304 cubic feet.