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

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(c) 3 \alpha % Let x be the radius, which is equal to the height of the cylinder. Let y be its volume. ∆ x/x $\times$ 100 = \alpha \text { Also }, y = $\pi$ x^2 x = $\pi$ x^3 \left[ \text{ Radius = Height of the cylinder }\right] \Rightarrow dy/dx = 3$\pi$ x^2 \Rightarrow ∆ y/y = 3$\pi$ x^2/ydx = 3/x $\times$ \alpha x/100 \Rightarrow ∆ y/y $\times$ 100 = 3\alpha \text { Hence, the error in the volume of the cylinder is } 3\alpha .%

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