Question

In the the diagram to the right, sphere O with radius 5 cm is intersected by a plane 4 cm from center O. Find the radiusof the cross section O A

Answer 1

Since a right triangle is formed, the radius of the cross-section is the missing side of the triangle.

Apply the Pythagorean theorem:

C^2 = a^2 + b^2

Where:

c = hypotenuse = 5

a & b = the other 2 legs of the triangle = 4 and x

Replacing:

5^2 = 4^2 + x^2

solve for x ( radius of the cross-section)

25 = 16 + x^2

25-16 = x^2

9 = x^2

√9 = x

x = 3 cm