PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# Solution for A Circular Metal Plate Expends Under Heating So that Its Radius Increases by K%. Find the Approximate Increase in the Area of the Plate, If the Radius of the Plate before Heating is 10 Cm. - PUC Karnataka Science Class 12 - Mathematics

#### Question

A circular metal plate expends under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.

#### Solution

Let at any time, x be the radius and y be the area of the plate.

$\text { Then,}$

$y = x^2$

$\text { Let ∆ x be the change in the radius and }\bigtriangleup y \text { be the change in the area of the plate }.$

$\text { We have }$

$\frac{∆ x}{x} \times 100 = k$

$\text { When }x = 10,\text { we get }$

$∆ x = \frac{10k}{100} = \frac{k}{10}$

$\text { Now,} y = \pi x^2$

$\Rightarrow \frac{dy}{dx} = 2\pi x$

$\Rightarrow \left( \frac{dy}{dx} \right)_{x = 10 cm} = 20\pi {cm}^2 /cm$

$\therefore ∆ y = dy = \frac{dy}{dx}dx = 20\pi \times \frac{k}{10} = 2k\pi \ {cm}^2$

Hence, the approximate change in the area of the plate is 2

$\pi$ cm2 .

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Solution A Circular Metal Plate Expends Under Heating So that Its Radius Increases by K%. Find the Approximate Increase in the Area of the Plate, If the Radius of the Plate before Heating is 10 Cm. Concept: Approximations.
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