Question

Please help me with the following question plus if it's possible picture demonstration will be easier for me to understand! ?

Answer 1

Area of spill is increasing at a rate of `1005.3` square feet per second.

Explanation:

Possible picture is as shown below:

As the spill is spreading at a rate of `4` feet per second, after `t` seconds, it will form a radius of `4t` feet and area of spill as a function of `t` would be

`A(t)=pi*(4t)^2=16pit^2`

and area of spill is increasing at a rate of

`(dA(t))/dt=32pit` square feet per second.

It will reach a radius of `40` feet in `40/4=10` seconds

and at that point area of spill will be increasing at a rate of

`(dA(10))/dt=32pi*10=320*3.1416=1005.3` square feet per second.