Question

The error in the measurement of volume of sphere is 1.5%. The error in the measurement of its diameter is?

Answer 1

Answer:

Please check the attachment above

Answer 2

Given :

The error in the measurement of the volume of a sphere is 1.5%.

To find :

The error in the measurement of its diameter.

Prerequisites :

As we know, the formula for the volume of a sphere is as :

V = $\frac{4}{3} \pi r^{3}$

where r represents radius , V represents volume of the sphere

Also, r = d/2

where d represents diameter of the sphere given.

Solution :

So, V = $\frac{4}{3} \pi \frac{d^{3} }{8}$

V = $\frac{1}{6} \pi d^{3}$

Now, considering the change, i.e, the delta as

where delta represents the change,

$\frac{Delta V}{V} = \frac{\frac{1}{6} \pi 3d^{3} Delta d}{\frac{1}{6}\pi d^{3} }$

$\frac{Delta V}{V} =\frac{3 Delta d}{d}$

Continuing further, converting it into a percentage

multiplying both the sides with 100,

$\frac{Delta V}{V} *100=\frac{3 Delta d}{d} *100$

Now, replacing $\frac{Delta V}{V} *100=1.5$

we get,

$\frac{Delta d}{d} *100= \frac{1.5}{3} =0.5$

Hence, the error in the measurement of its diameter is 0.5 %.

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