Find the rate of change of the area of a circle when its radius is 18.0 m and the radius is changing at the rate of 10.1 cm/s?
rate in m2/s =
My attempt....
dA/ dt = Pie R^2 * dr/dt
10.1cm/s = pie (1800cm) * dr/dt
dr/dt = 0.0101/pie 3240 * m^3/m^2
dr/dt = 0.0101/pie 3240 m2/s
Can you confirm...
Thanks
To find the rate of change of the area of a circle, we can use the formula:
dA/dt = π * (2 * r) * (dr/dt)
Where dA/dt is the rate of change of the area, r is the radius, and dr/dt is the rate of change of the radius.
Given that the radius is changing at a rate of 10.1 cm/s, we need to convert the units to meters:
dr/dt = 10.1 cm/s * (1 m / 100 cm) = 0.101 m/s
Now let's substitute the values into the formula:
dA/dt = π * (2 * 18.0 m) * (0.101 m/s)
= π * 36.0 m * 0.101 m/s
≈ 11.44π m^2/s
So, the rate of change of the area of the circle is approximately 11.44π m^2/s.