Question

what is the percentage error in the volume of a sphere when the error in the radius of the sphere is 2%​

Answer 1

▶ Solution :

Given :

▪ Percentage error in the radius of sphere is 2%

To Find :

▪ Percentage error in the volume of sphere.

Formula :

→ Formula of volume of the sphere :

☞ V = (4/3)π R^3

→ Formula of percentage error :

☞ %(ΔV/V) = 3(ΔR/R) × 100

Calculation :

→ %(ΔV/V) = 3(ΔR/R) × 100

→ %(ΔV/V) = 3(2%)

→ %(ΔV/V) = 6%

Answer 2

let the radius of sphere=r

volume of sphere v=4/3πr3

error in measurement of radius=2•\•

there fore=∆r/r=2•\•

error volume∆v/v=4/3πrx3r2x∆r/4/3πr2.

=3∆r=3x0.02

=0.06

=6•\•

Answer is=6•\•

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