Find Maximum Percentage Error Using Radius of Sphere

 

❓ Question

The radius of a sphere is measured as

$$r=(7.50\pm0.85)\text{ cm}$$

Find the percentage error in the volume of the sphere.

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✍️ Solution

Volume of a sphere is

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

For maximum fractional error,

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

Therefore, percentage error is

$$\frac{\Delta V}{V}\times100 = 3\frac{\Delta r}{r}\times100$$

Substituting the values,

$$\frac{\Delta V}{V}\times100 = 3\times\frac{0.85}{7.50}\times100$$
$$= 3\times11.33$$
$$=34\%$$

✅ Final Answer

$$\boxed{34\%}$$