Question

A circular disc of radius 3 cm is being heated due to expansion its radius increases at the rate of 0.05 m per second find the rate at which its area is increasing when radius is 3.2 cm

Answer 1

ATTACHMENT...........✌
MARK BRAINLIEST

Answer 2

Given :

The radius of circular disc = 3 cm

The rate of increase in radius = 0.05 m/s

To Find :

The rate of increase in area when, radius = 3.2 cm

Solution :

Since, Area of circular disc = A = π × radius²

Or,       A = π × r²

As  rate of increase in radius = 0.05 m/s

i.e  $\dfrac{dr}{dt}$ = 0.05 m/s

So, rate of change of area = $\dfrac{dA}{dt}$

Or,  $\dfrac{dA}{dt}$  = π × $\dfrac{dr^{2} }{dt}$

Or,  $\dfrac{dA}{dt}$  = π × $\dfrac{dr^{2} }{dr}$ ×  $\dfrac{dr^{} }{dt}$

Or, $\dfrac{dA}{dt}$  = 3.14 × 2 r ×  $\dfrac{dr^{} }{dt}$

Or, $\dfrac{dA}{dt}$  = 3.14 × 2 × 3.2 cm ×  0.05 m/s

Or, $\dfrac{dA}{dt}$  = 3.14 × 2 × 0.032 m ×  0.05 m/s             ( 1 cm = 0.01 m )

∴   $\dfrac{dA}{dt}$ = 0.010048 m/s

So, The rate of change in area =  $\dfrac{dA}{dt}$ = 0.010048 m/s

Hence, The rate of change in area of disc is 0.010048 m/s  Answer