Question

9.
1. If the error in the measurement of radius of a sphere
is 2%, then the error in the determination of volume of the
sphere will be
(a) 8% (b) 2% (c) 4%
(d) 6%
​

Answer 1

Answer:

D.) 6%

Step-by-step explanation:

Given:

• the error in the measurement of radius of a sphere is 2%.

To find:

• The error in the determination of volume of the sphere.

Solution:

V = 4/3 π r³

Where,

Volume of sphere

Take logarithm on both sides,

• log V = log 4/3 π r³
• log V = log 4/3 π + 3 log r

Differentiating,

• ∆V/V = 0 + 3∆r/r

We have:

∆r/r = 2%

Now,

• ∆V/V = 0 + 3 × 2%
• ∆V/V = 6%

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