Question

The radius of a sphere is expressed as (5.0+0.1) cm. Find the volume of the sphere with
error. Also determine percentage error.

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Answer 1

Given that,

$\large\rm {\bigstar ∆r = 0.1 \ cm}$

$\large\rm {\bigstar r = 5.0 \ cm}$

To find :

✓Volume

✓Percentage error

Solution:

The volume is given as

$\large\rm { V = (4/3) πr³}$

$\large\rm { V = (4/3) × 3.14 × 5.1}$

Thus,

$\large\boxed{\rm { V = 555.36552}}$

Now, the error equation,

$\large\rm { ∆V /V = 3(∆r/r) }$

$\large\rm { ∆V = V \times 3(∆r/r)}$

Thus,

$\large\rm { ∆V = 555.36 × 3 × (0.1/5.0)}$

$\large\rm { ∆V = 33.32 cm^{3}}$

Thus,

$\large\rm { ∆V /V × 100 = (33.32/555.36) × 100}$

Thus,

$\large\boxed {\rm { ∆V/V × 100 = 5.99 (approx) }}$

$( \ddot\smile )$ Hope it helped.