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The radius of a sphere whose centre is (4, 4, -2) and which passes through the origin is:

The radius of a sphere whose centre is (4, 4, -2) and which passes through the origin is: Correct Answer 6

Concept:

The distance 'd' between two points (x1, y1, z1) and (x2, y2, z2) in space is obtained by using the Pythagoras' Theorem twice:

d2 = (x1 - x2)2 + (y1 - y2)2 + (z1 - z2)2

Calculation:

Radius of a sphere is the distance between the centre of the sphere to any point on its surface.

Here the center is given to be (4, 4, -2) and the origin (0, 0, 0) is given to be a point on its surface.

∴ r2 = (4 - 0)2 + (4 - 0)2 + (-2 - 0)2 = 16 + 16 + 4 = 36

⇒ r = 6.

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