If an error of 0 . 02 sq . cm is found in the surface area of a sphere when its radius is measured as 10 cm , then the approximate error that occurs in the volume of the sphere, in cubic centimetres, is

Question

If an error of 0 . 02 sq . cm is found in the surface area of a sphere when its radius is measured as 10 cm , then the approximate error that occurs in the volume of the sphere, in cubic centimetres, is, 0 . 2, 0 . 01, 0 . 3, 0 . 1

MARKS App · Accepted Answer

Surface area of sphere, S = 4 π r 2 ∆ S = 8 π r ∆ r Given ∆ S = 0 . 02 sq . cm at r = 10 cm So, ∆ r = 0 . 02 8 π × 10 = 0 . 001 4 π cm Volume of sphere, V = 4 3 π r 3 i.e. ∆ V = 4 π r 2 ∆ r = 4 π × 10 2 × 0 . 001 4 π = 0 . 1 cm 3

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