Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
If the radius of a sphere is measured as with an error of then, find the approxi
If the radius of a sphere is measured as \( 9 \mathrm{cm} \) with an error of \( 0.03 \mathrm{cm} \) then, find the approximate error in calculating its volume
- A. \( 9.72 \pi \mathrm{cm}^{3} \)
- B. \( 7.92 \pi \mathrm{cm}^{3} \)
- C. \( 8.72 \pi \mathrm{cm}^{3} \)
- D. None of these
Step-by-step solution
Volume of sphere V = (4/3)πr^3. Differentiating, dV = 4πr^2 dr. Given r = 9 cm and dr = 0.03 cm, so dV = 4π(81)(0.03) = 9.72π cm^3.
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