KCET2014MathematicsFunctions
A stone is dropped into a quiet lake and waves move in circles at the speed of ( 5 cms ⁻¹ ). At that instant, when the radius of circular wave is ( 8 ~cm ), how fast is the enclosed area increasing?
Options
- A( 8 cm ² s⁻¹ )
- B( 80 cm ² s⁻¹ )
- C( 6 cm ² s⁻¹ )
- D( 0 8 3 ~cm ² s⁻¹ )
Correct answer
B. ( 80 cm ² s⁻¹ )
Step-by-step solution
Given that, ( d r d t =5 cms ⁻¹ ) and area of circle is given by ( A= r² ) So, ( d A dt = 2 r d r d t =2 (8) 5=80 Cm ² ~s ⁻¹ )