A water tank is in the shape of a sphere of radius 10 feet. The tank is supported on a metal circle 8 feet below the center of the sphere, as shown in the figure. Find the radius of the metal circle
A) $6 \mathrm { ft }$
B) $2 \mathrm { ft }$
C) $3 \mathrm { ft }$
D) $5 \mathrm { ft }$
E) none of these

Question

Quizplus · Accepted Answer

The radius of the metal circle can be found using the Pythagorean theorem in a right triangle formed by the radius of the sphere, the distance from the center of the sphere to the metal circle, and the radius of the metal circle. Given the radius of the sphere is 10 feet and the distance from the center to the circle is 8 feet, we have $10^2 = 8^2 + r^2$, solving for $r$ gives $r = 6$ feet.

A Water Tank Is in the Shape of a Sphere 6ft6 \mathrm { ft }6ft

A Water Tank Is in the Shape of a Sphere $6 \mathrm { ft }$