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# Solution for If the Radius of a Sphere is Measured as 9 Cm with an Error of 0.03 M, Find the Approximate Error in Calculating Its Surface Area ? - CBSE (Commerce) Class 12 - Mathematics

#### Question

If the radius of a sphere is measured as 9 cm with an error of 0.03 m, find the approximate error in calculating its surface area ?

#### Solution

Let x be the radius and be the surface area of the sphere.

$\text { Then },$

$x = 9$

$∆ x = 0 . 03 m = 3cm$

$\Rightarrow x + ∆ x = 9 + 3 = 12 cm$

$y = 4 \pi x^2$

$\text { For } x = 9,$

$y = 4\pi \times 9^2 = 324\pi$

$\frac{dy}{dx} = 8\pi x$

$\Rightarrow \left( \frac{dy}{dx} \right)_{x = 9} = 72\pi$

$\therefore ∆ y = dy = \frac{dy}{dx}dx = 72\pi \times 3 = 216\pi {cm}^2$

$\text { Therefore, the approximate error in the surface area is} 216\pi c m^2 .$

$\text { Disclaimer: This solution has been created according to the question given in the book . However, the solution given in the book is incorrect } .$

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Solution If the Radius of a Sphere is Measured as 9 Cm with an Error of 0.03 M, Find the Approximate Error in Calculating Its Surface Area ? Concept: Approximations.
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