Question

1. A restaurant supplier services the restaurants in a circular area in such way that the radius r is increasing at the rate of 2 miles per year at the moment when r = 5 miles. How fast is the area increasing?

Answer 1

Answer:

A= π*r²

dA/dt= π*r*dr/dt

dA/dt= π*5*2= 10π km/yr

Answer 2

Using implicit differentiation, it is found that the area is increasing at a rate of 62.8 miles squared per year.

The area of a circle of radius r is given by:

$A = \pi r^2$

Applying implicit differentiation, the rate of change is given by:

$A = 2r\pi \frac{dr}{dt}$

In this problem:

• Radius increasing at a rate of 2 miles per year, hence $\frac{dr}{dt} = 2$.
• Moment of a radius of 5 miles, hence $r = 5$.

Then:

$A = 2r\pi \frac{dr}{dt}$

$A = 2(5)\pi(2)$

$A = 62.8$

The area is increasing at a rate of 62.8 miles squared per year.

A similar problem is given at https://brainly.com/question/9543179