Question

A sphere of radius 13 cm is cut by a plane whose distance from the center of the sphere is 5 cm. What is the circumference of the plane circular section?

(a) 10 π  cm 

(b) 12 π  cm 

(c) 24 π  cm 

(d) 26 π  cm

Answer 1

Answer: (c) = 24π 

Let O be the center of the sphere and let A be the center of the circular plane. 

Then radius (r) of the plane

= \(\sqrt{13^2 -5^2} = \sqrt{169-25} =\sqrt{144}\) 

= 12 cm

∴  Circumference of the plane circular section = 2πr 

= 2×π×12 cm 

= 24π cm.