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morrisjillian23
29.07.2020 •
Mathematics
In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all directions. Assuming that the area polluted is a circle and that its radius is increasing at a rate of 3ft/sec, determine how fast the area is increasing when the radius of the circle is 30 feet. Hint: consider that the radius r is a function, and we know the rate of change of r with respect to time.
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Ответ:
Step-by-step explanation:
Since the area pollute sis assumed to be a circle, we will be using the formula for calculating the area of a circle to solve the problem.
Area of a circle A = πr²
r is the radius of the circle
The rate at which the area is increasing is expressed as dA/dt. According to chain rule, dA/dt = dA/dr*dr/dt where;
dr/dt is the rate at which the area is increasing.
If dA/dr = 2πr (by mere differentiation)
dA/dt = 2πr * dr/dt
Given dr/dt = 3ft/sec and r = 30feet
dA/dt = 2π(30) * 3
dA/dt = 180π ft/sec
Hence, the area is increasing at the rate of 180π ft/sec
Ответ:
0.15590200
Step-by-step explanation: