You're standing 14 feet from the edge of a cylindrical water tank and is 26 feet from the point of tangency. the tank is 10 feet tall. what is the volume in cubic feet

To find the volume of the cylindrical water tank, we first need to calculate the radius of the base.

Let's denote:
x = distance from the edge of the tank to the point of tangency.

Given:
You are standing 14 feet from the edge of the tank, so the distance from the edge to the point of tangency (x) can be calculated by subtracting the given distance from your position to the point of tangency (26 feet) from the distance from the edge to your position (14 feet).
x = 26 - 14 = 12 feet

Now, we can calculate the radius (r) of the base of the tank. Using the Pythagorean theorem, we have:
r^2 = x^2 + h^2
r^2 = 12^2 + 10^2
r^2 = 144 + 100
r^2 = 244

Taking the square root of both sides, we get:
r ≈ √244
r ≈ 15.62 feet (rounded to two decimal places)

Finally, we can calculate the volume (V) of the cylindrical water tank using the formula for the volume of a cylinder:
V = π * r^2 * h
V = π * (15.62)^2 * 10
V ≈ π * 243.87 * 10
V ≈ 7679.93 cubic feet (rounded to two decimal places)

Therefore, the volume of the cylindrical water tank is approximately 7679.93 cubic feet.

To find the volume of the cylindrical water tank, you need to know the radius of the tank and its height.

Let's begin by finding the radius of the tank. We are given that we are standing 14 feet from the edge of the tank, which is the distance from the center of the tank to the point of tangency. This is also called the radius of the tank.

Using the Pythagorean theorem, we can calculate the radius as follows:

radius^2 + distance from the point of tangency^2 = distance from the center of the tank^2

radius^2 + 14^2 = 26^2

radius^2 + 196 = 676

radius^2 = 676 - 196

radius^2 = 480

Taking the square root of both sides, we find:

radius = √480 ≈ 21.91 feet

Now that we have the radius, we can calculate the volume of the cylindrical tank using the formula:

Volume = π * radius^2 * height

Where π (pi) is approximately 3.14.

In this case, the height of the tank is given as 10 feet, so we can substitute in the values to find the volume:

Volume = 3.14 * (21.91)^2 * 10

Volume ≈ 3.14 * 480 * 10

Volume ≈ 15072 cubic feet

Therefore, the volume of the cylindrical water tank is approximately 15072 cubic feet.

The radius of the tank can be found using

26^2 = 14^2 + r^2
r^2 = 480

since the radius is perpendicular to any tangent line.

Now just plug in
v = pi*r^2*h
= pi*480*10