Sphere word problem//geometry

Question

How long is a chord of a sphere that connects orthogonal radii of 8”? Show all your calculations and an explanation as to whether or not your answer is reasonable. Leave your answer in simplest radical form.

Answer 1

Hi Sarah,

Since the radii of length r are orthogonal, the central angle C is 90°. The expression for the chord length is

L = 2∗r∗sin (C/2)

Substitute the central angle C = 90

L = 2∗r∗sin(90/2)

Since 90/2 = 45

L = 2∗r∗sin(45)

Now substitute the radius of 8

L = 2∗8∗sin(45)

Since 8∗2 = 16 and sin(45) = √2/2

L = 16∗√2/2

Giving the final chord length

L = 8√2 = 11.3"

Hope this helps,

Ali