APPLICATION OF DERIVATIVES

TWO/THREE/FIVE MARK QUESTIONS:

1) Find the rate of change of the area of a circle w.r.t to its radius ‘r’

when r = 4 cm?

Ans: Area of circle A = r

2

, dA/dr = ? when r = 4 cm

Differentiate w.r.t. ‘r’

dA/dr = (2r)

= (2)(4)

= 8 sq. cms

Therefore area of the circle is increasing at the rate of 8 sq. cms.

2) An edge of a variable cube is increasing at the rate of 3cm/s. How fast is

the volume of the cube increasing when the edge is 10cm long?

Ans: Volume of a cube V = x

3

., Given: dx/dt = 3cm/s. dV/dt = ?

when x = 10cm

Didifferentiate w.r.t ‘t’

dV/dt = 3x

2

(dx/dt)

= 3(10)

2 . (3)

= 900 c.c/s

Therefore volume of the cube increasing at the rate of 900 c.c/s.

Download Tag | Mathematics, PUC Notes |

Download Category | PUC Karnataka |

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