Question

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

Answer 1

i think not to sure

6 sqrt 2

Answer 2

Answer:

Hence, the length of the chord joining two perpendicular radii is:

6√2 inches.

Step-by-step explanation:

Let r denote the radius of circle.

i.e. r=6 inches.

Let AB be the chord that connects two perpendicular radii i.e. OA and OB whose lengths are given to be 6 inches.

We can apply pythagorean theorem to find the length of the chord.

$AB^2=OA^2+OB^2\\\\AB^2=6^2+6^2\\\\AB^2=36+36\\\\AB^2=72\\\\AB=\sqrt{72}\\\\AB=6\sqrt{2}$.

Hence, the length of a chord connecting two perpendicular radii is:

6√2 inches.