Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
If the ratio of base radius and height of a cone is 1: 2 and percentage error in
If the ratio of base radius and height of a cone is 1: 2 and percentage error in radius is \( \lambda \%, \) then the error in its volume is
- A. \( \lambda \% \)
- B. 2\lambda\%
- C. \( 3 \lambda \% \)
- D. none of these
Step-by-step solution
Given r:h = 1:2, so h = 2r. Volume V = (1/3)πr²h = (1/3)πr²(2r) = (2/3)πr³. Thus V ∝ r³. Percentage error in V is 3 times percentage error in r, i.e., 3λ%.
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