Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
The height of a cylinder is equal to the radius. If an error of is made in the h
The height of a cylinder is equal to the radius. If an error of \( \alpha \% \) is made in the height, then percentage error in its volume is
- A. \( \alpha \% \)
- B. \( 2 \alpha \) \%
- C. 3 \alpha \% \)
- D. none of these
Step-by-step solution
Given height h = radius r, volume V = πr^2h = πr^3. An error of α% in height implies Δh/h = α/100. Since h = r, we also have Δr/r = α/100 (as radius is same as height). The percentage error in volume is approximately (ΔV/V) × 100 = (2Δr/r + Δh/h) × 100 = (2α/100 + α/100) × 100 = 3α%.
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