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# Solution for If the Radius of a Sphere is Measured as 7 M with an Error of 0.02 M, Find the Approximate Error in Calculating Its Volume ? - CBSE (Science) Class 12 - Mathematics

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#### Question

If the radius of a sphere is measured as 7 m with an error of 0.02 m, find the approximate error in calculating its volume ?

#### Solution

Let x be the radius of the sphere and y be its volume.

$y = \frac{4}{3}\pi x^3$

$\text { Let ∆ x be the error in the radius } .$

$x = 7$

$∆ x = 0 . 02$

$\frac{dy}{dx} = 4\pi x^2$

$\Rightarrow \left( \frac{dy}{dx} \right)_{x = 7} = 196\pi$

$\therefore ∆ y = dy = \frac{dy}{dx}dx = 196\pi \times 0 . 02 = 3 . 92\pi$

$\text { Hence, the approximate error in calculating the volume of the sphere is } 3 . 92\pi m^3 .$

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Solution If the Radius of a Sphere is Measured as 7 M with an Error of 0.02 M, Find the Approximate Error in Calculating Its Volume ? Concept: Approximations.
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