AP EAMCET202022 Sep 2020Morning ShiftMathematicsDifferential EquationsActual
The radius of a circle is increasing at a rate of 0.1 ~cm ~s ⁻¹ . Then the rate of change of area, when its radius is 5 ~cm , is .........
Options
- A^2 ~cm ^2 ~s ⁻¹
- Bcm ^2 ~s ⁻¹
- C2 cm ^2 ~s ⁻¹
- D2 ~cm ^2 ~s ⁻¹
Correct answer
B. cm ^2 ~s ⁻¹
Step-by-step solution
Let the circle have radius r ~cm and area A ~cm ^2 and it is given that d r d t =0.1 ~cm . s ⁻¹ and as we know area A= r^2 d A d t =2 r d r d t Rate of change of area, when radius is 5 ~cm is . d A d t |_ r=5 ~cm =2 (5)(0.1)= cm ^2 s ⁻¹