Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
If metallic circular plate of radius is heated so that its radius increases at t
If metallic circular plate of radius \( 50 \mathrm{cm} \) is heated so that its radius increases at the rate of \( 1 \mathrm{mm} \) per hour, then the rate at which the area of the plate increases \( \left(\operatorname{in} c m^{2} / h r\right) \) is
- A. \( 5 \pi \)
- B. \( 10 \pi \)
- C. \( 100 \pi \)
- D. \( 50 \pi \)
Step-by-step solution
Area of circular plate A = πr^2. Given dr/dt = 1 mm/hr = 0.1 cm/hr. Then dA/dt = 2πr dr/dt. At r = 50 cm, dA/dt = 2π × 50 × 0.1 = 10π cm^2/hr.
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