KCET2015MathematicsStatistics
A balloon which always remains spherical is being inflated by pumping in ( 10 ) cubic centimeters of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is ( 15 cms ).
Options
- A( 1 90 cm s⁻¹ )
- B( 1 9 cm s⁻¹ )
- C( 1 30 cm s⁻¹ )
- D( 1 cm s⁻¹ )
Correct answer
A. ( 1 90 cm s⁻¹ )
Step-by-step solution
As we know that, the volume of sphere is given by [ V= 4 3 r³ ] [ array l So, d V d t =4 r² d r d t Here d V d t =10 ~cm ³ ~s ⁻¹ and r=15 ~cm we get 10=4 (15)² d r d t d r d t = 10 4 (15² ) = 1 90 array ]