The radius of a sphere is 6 inches. Find the length of a chord connecting two perpendicular radii.

Solution:

It is given that

Radius of a sphere = 6 inches

We know that

The chord and radii together make an isosceles right triangle with 6 inches legs.

By using pythagoras theorem, we get

AB² = 6² + 6²

AB = √72

AB = 6√2

So the hypotenuse would be √2 times the length of the leg.

The chord will be 6√2 inches in length.

Therefore, the length of the chord is 6√2 inches.

The radius of a sphere is 6 inches. Find the length of a chord connecting two perpendicular radii.

Summary:

The radius of a sphere is 6 inches. The length of a chord connecting two perpendicular radii is 6√2 inches.