Calculus Question

Question

A rectangle has one side of 10 cm. How fast is the area of the rectangle changing at the instant when the other side is 42 cm and increasing at 7 cm per minute? Include units

1. At that instant, the area of the rectangle is changing at a rate of ______

Answer 1

Let the area of the rectangle be A = L.w , where L is the length and w is the width.

Note that in your problem you are given that one side is 10 cm and the other is 42 cm , Since in a recatangle the length L is always greater than the width, then L > w and the length is L = 42 cm, the width w = 10 cm. you are required to find the change of area wrt to time dA/dt

now L/w = 42/10, and 10 L = 42 w, solving for w = 10/42 L = 5/21 L

The area is A = L.w = L ( 5/21 L) = 5/21 L²

and dA / dt = 5/21 . 2. L. dL /dt , You are given dL/dt = 7cm /min, substitute in equation and you get:

dA / dt = 5/21 . 2. L . 7 cm/min = 3.333 cm/min. L , recall that L = 42 cm at the instant w = 10 cm

dA/dt = 3.333 cm/min. ( 42 cm) = 140 cm² / min