Chapter 9.3, Problem 21E

Spherical Water Tank A water tank is in the shape of a sphere of radius 5 ft. The tank is supported on a metal circle 4 ft below the center of the sphere, as shown in the figure. Find the radius of the metal circle.

To determine

To Find: The radius of the metal circle.

Answer to Problem 21E

The radius of the metal circle on which the water tank gets support is 3 feet.

Explanation of Solution

Given:

The value of radius of the spherical tank is 5 ft and the metal circle is 4 ft below the center of the tank.

Calculation:

The below figure is of the spherical tank.

Figure (1)

Use Pythagorean theorem in the triangle $AOB$.

$\begin{array}{l}{\left(OA\right)}^2={\left(OB\right)}^2+{\left(AB\right)}^2\\ {\left(AB\right)}^2={\left(OA\right)}^2-{\left(OB\right)}^2\end{array}$

Substitute 5 for OA, 4 for OB in the above expression to get the value of AB.

$\begin{array}{c}{\left(AB\right)}^2={\left(5\right)}^2-{\left(4\right)}^2\\ =25-16\\ =9\end{array}$

Take square root both sides to get the value of AB.

$\begin{array}{c}\sqrt{{\left(AB\right)}^2}=\sqrt{9}\\ AB=3\end{array}$

Thus, the radius of the metal circle on which the water tank gets support is 3 feet.