Question

A plane x + 2y + 2z – 15 = 0 cuts a sphere x² + y² + z² – 2y – 4z – 11 = 0 in a circular section. What is the radius of the cut section?

• (A) √2 units
• (B) √5 units
• (C) 3 units
• (D) √7 units

Answer 1

The Correct Option is D

Explanation:
since, the centre of sphere $x^2+y^2+z^2-2y-4z-11=0$ is (0,1,2) andradius is 4$\therefore$ Distance of a plane $x+2y+2z-15=0$from (0,1,2)$=\frac{|0+2+4-15|}{\sqrt{1+4+4}}$$=\frac{9}{3}=3$$=\sqrt{4^2-3^2}=\sqrt{16-9}=\sqrt{7}$Radius of circle $=\sqrt{7}$