Question

STORAGE A cylindrical tank is placed along a wall.

A cylindrical PVC pipe will be hidden in the corner
behind the tank. See the side view diagram below.
The radius of the tank is r inches and the radius of the
PVC pipe is s inches.
Wall-
Pipe
Tank
Floor
a. Use the Pythagorean Theorem to write an equation
for the relationship between the two radii. Simplify
your equation so that there is a zero on one side of
the equals sign.

Answer 1

Explanation:

In the side view diagram, we can see that the tank, the wall, and the floor form a right triangle with the radius of the tank as the hypotenuse. Let x be the distance between the tank and the wall, as shown below:

```

|\

| \

r | \ x

| \

|_ _\

s

```

Using the Pythagorean theorem, we can write:

r^2 = x^2 + s^2

Rearranging this equation, we get:

x^2 = r^2 - s^2

Subtracting r^2 from both sides, we get:

x^2 - r^2 = -s^2

Multiplying both sides by -1, we get:

s^2 - x^2 = 0

Therefore, the equation for the relationship between the two radii is:

s^2 - x^2 = 0

Simplifying this equation, we get:

s^2 = x^2

or

x^2 = s^2

So, there is a zero on one side of the equals sign.