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# Solution for The Height of a Cylinder is Equal to the Radius. If an Error of α % is Made in the Height, Then Percentage Error in Its Volume is (A) α % (B) 2α % (C) 3α % (D) None of These - CBSE (Commerce) Class 12 - Mathematics

#### Question

The height of a cylinder is equal to the radius. If an error of α % is made in the height, then percentage error in its volume is
(a) α %
(b) 2α %
(c) 3α %
(d) none of these

#### Solution

(c) 3 $\alpha$

Let x be the radius, which is equal to the height of the cylinder. Let y be its volume.

$\frac{∆ x}{x} \times 100 = \alpha$

$\text { Also }, y = \pi x^2 x = \pi x^3 \left[ \text{ Radius = Height of the cylinder }\right]$

$\Rightarrow \frac{dy}{dx} = 3\pi x^2$

$\Rightarrow \frac{∆ y}{y} = \frac{3\pi x^2}{y}dx = \frac{3}{x} \times \frac{\alpha x}{100}$

$\Rightarrow \frac{∆ y}{y} \times 100 = 3\alpha$

$\text { Hence, the error in the volume of the cylinder is } 3\alpha % .$

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: 4 | Page no. 13

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Solution for question: The Height of a Cylinder is Equal to the Radius. If an Error of α % is Made in the Height, Then Percentage Error in Its Volume is (A) α % (B) 2α % (C) 3α % (D) None of These concept: Approximations. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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