Question

the radius of a circle is increasing at a rate of 4 cm/s. how fast is the area of the circle increasing after 10 seconds? g

Answer 1

A = 1600π cm²

Explanation:

Pre-Solving

We are given that a circle's radius increases 4 cm every second.

We want to know how large the area of the circle is after 10 seconds.

Solving

We first need to find how large the radius will be.

We know the proportion of the rate increase / time; for every 1 second, the rate increases by 4 cm.

We can write this as a proportion:

`(4 cm)/(1 s) = (x)/(10s)`

We can cross multiply to get:

4 cm * 10 s = x * 1 s

Divide both sides by 1 s

(4 cm * 10 s) / (1 s) = 40cm = x

So, after 10 seconds, the radius will be 40cm.

We aren't done yet though, remember that the question wants us to find the area of the circle.

The area can be calculated using the equation A = πr², where r is the radius.

We can substitute 40 as r in the equation to get:

A = πr² = π * (40)² = 1600π cm²