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# The area of a circle is increasing at a rate of 4ft /min.How fast is the radius of this circle increasing at the instant the area is 16π ft?

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- Pramod KumarLv 71 month ago
Area (A) of a circle is = π R² where R = radius of the circle.

=> A = π R²

When Area = 16π, R = 4 ft ......................... (1)

Differentiate both the sides with respect to Time (t),

dA/dt = 2 π R dR/dt

dA = Rate of change in area = 4 ft² /min and Radius = 4 ft ..... (from 1 above )

=> Rate of change in Area = ( 2 π R ) * Rate in change of Radius.

=> 4 = 2 π 4 ( dR/dt)

=> dR/dt = 1/(2π) ft/min ........ Answer

- 1 month ago
dA/dt = 4

A = pi * r^2

dA/dt = 2 * pi * r * dr/dt

A = 16 * pi

16 * pi = pi * r^2

16 = r^2

4 = r

dA/dt = 2 * pi * r * dr/dt

4 = 2 * pi * 4 * dr/dt

1/(2pi) = dr/dt

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