Question

Find rate of change in area of a square of side 4 cm then its side is increasing at the rate of 0.1 cm per second​

Answer 1

Answer:

rate of change in area of square = 0.8ms²

Explanation:

To find,

dA/dt

Given that,

the side of square is increasing at the rate of 0.1 cm/s

let side of square be a

and area be A

so,

da/dt = 0.1 cm/s. ....(1)

now,

A = a² [area of square ]

so,

change in area with respect to its side

= dA/da

= d(a²)/da

after differentiation we get

dA/da = 2a

now,

change in area with respect to time

= dA/dt

= (dA/da)(da/dt)

from (1)

da/dt = 0.1 cm/s

putting the values,

dA/dt = 2a × 0.1

since side of square a = 4 CM so,

dA/dt = 2(4) × 0.1

= 8 × 0.1

dA/dt = 0.8 cm/s²

so,

rate of change in area of square

= 0.8 m/s²

Answer 2

Answer:

rate of change in area of square

= 0.8 m/s²

explanations refer to attachment

sorry for bad handwriting