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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. - CBSE (Commerce) Class 12 - Mathematics

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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 .

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (with solutions)
Chapter 14: Differentials, Errors and Approximations
Q: 3 | Page no. 9

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Solution for 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. concept: Approximations. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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