Answer:
A) dA/dt = 2πr(dr/dt)
B) dA/dt = 50π m²/s
Explanation:
A) The formula for Area is;
A = πr²
Since, we want to find dA/dt. Thus,
(A)(1/dt) = (πr²)(1/dt)
Thus, differentiating;
(dA/dr)(1/dt) = 2πr(1/dt)
Multiply both sides by dr to obtain;
dA/dt = 2πr(dr/dt)
(b) we want to find rate of area (dA/dt) when r = 25m and dr/dt = 1 m/s
since we know that, dA/dt = 2πr(dr/dt), we can solve it as;
dA/dt = 2π(25)(1)
dA/dt = 50π m²/s
The area of the spill is increasing at a rate of 157m²/s
The formula for calculating the area of the circle is expressed as:
[tex]A = \pi r^2[/tex]
The rate at which the area of the spill is increasing is expressed as:
[tex]\frac{dA}{dt} =\frac{dA}{dr}\cdot\frac{dr}{dt} \\\frac{dA}{dt} =2 \pi r\cdot\frac{dr}{dt}[/tex]
Given the following parameters
radius r = 25 m
[tex]\frac{dr}{dt} =1m/s[/tex]
Substitute the given parameters into the formula:
[tex]\frac{dA}{dt} = 2(3.14)(25)(1)\\ \frac{dA}{dt} =157m^2/s[/tex]
Hence the area of the spill is increasing at a rate of 157m²/s
Learn more here: https://brainly.com/question/12810047
