Home
Class 12
MATHS
The rate of change of the area of a circ...

The rate of change of the area of a circle with respect to its radius r at `r = 6`cm is
(A) `10pi`
(B) `12pi`
(C) `8pi`
(D) `11pi`

Text Solution

Verified by Experts

Area of a circle `A = pir^2`
`:.` Rate of change of area with respect to radius, `(dA)/(dr) = 2pir`
At `r = 6`, Rate of change, `((dA)/(dr))_(r=6) = 2pi**6 = 12pi cm^2.`
Promotional Banner

Similar Questions

Explore conceptually related problems

The rate of change of area of circle with respect to its radius r at r =3 cm is :

Find the rate of change of the area of a circle with respect to its radius when r =4 cm .

Find the rate of change of area of a circle with respect to its radius 'r' when r=7cm.

Find the rate of change of the area of a circle with respect to its radius r when r=5c mdot

Find the rate of change of area of the circle with respect to its radius 'r' when r=3.5 cm.

Find the rate of change of the area of a circle with respect to its radius r when(a) r = 3 c m (b) r = 4 c m

What is the area of circle with a circumference of 10pi ?

What is the radius of a circle with an area of (pi)/(4) ?

Find the area of a circle of radius 30 cm (use pi=3.14 )

The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder, in c m^2//m in , when the radius is 2c m and the height is 3cm is (a) -2pi (b) -(8pi)/5 -(3pi)/5 (d) (2pi)/5