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Dovator [93]
3 years ago
10

The radius of a sphere is measured to be 3.0 inches. If the measurement is correct within 0.01 inches, use differentials to esti

mate the error in the volume of sphere.
Mathematics
1 answer:
Zarrin [17]3 years ago
5 0

Answer:

ΔV = 0.36π   in³

Step-by-step explanation:

Given that:

The radius of a sphere = 3.0

If the measurement is correct within 0.01 inches

i.e the change in the radius Δr = 0.01

The objective is to use differentials to estimate the error in the volume of sphere.

We all know that the volume of a sphere

V =  \dfrac{4}{3} \pi r^3

The differential of V with respect to r is:

\dfrac{dV}{dr }= 4 \pi r^2

dV = 4 πr² dr

which can be re-written as:

ΔV = 4 πr² Δr

ΔV = 4 × π × (3)² × 0.01

ΔV = 0.36π   in³

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