#### 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?

Solution 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.