Application of DerivativeMedium

Question

The surface area of a spherical bubble is increasing at the rate of 2 cm2/s. When the radius of the bubble is 6 cm, then the rate by which the volume of the bubble increasing is-

Options

A.6 cm3/sec
B.9 cm3/sec
C.3 cm3/sec
D.12 cm3/sec

Solution

A = 4πr2
⇒  = 8 π r
⇒  2 = 8 . π . 6 .
[∵ = 2cm2/sec    &    r = 6 cm]
⇒ cm/sec
Now V = π r3
⇒ ⇒  4 . π r2
⇒  
⇒  = 6 cm3/sec.

Create a free account to view solution

View Solution Free
Topic: Application of Derivative·Practice all Application of Derivative questions

More Application of Derivative Questions

The radius of a circle is increasing at the rate of 0.7 cm/sec. The rate of increase of its circumference is -...For the function f(x) = x cot-1x, x ≥ 0...The equation of normal to the curve y = ex at the point (0, 1) is-...An inverted cone has a depth of 10 cm and a base of radius 5 cm. Water is poured into it at the rate of 3/2 c.c. per min...The line x/a + y/b = 1 touches the curve y = be−x/a at the point-...