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ivanzaharov [21]
3 years ago
9

The area of a circle is increasing at the rate of pi cm^(2)/min. At what rate is the radius increasing when the area is 4pi cm^(

2)?
Mathematics
1 answer:
Vikentia [17]3 years ago
3 0
This problem deals the rate of change.
For the formula of the area of a circle, we differentiate both sides with respect to time t.
(A = πr^2) d/dt
dA/dt = 2πr (dr/dt)

Since we don't know yet the radius r, the area of a circle is given.
A = πr^2
r^2 = A/π = 4π/π
r^2 = 4
r = 2 cm

Therefore, the rate of the radius is
dA/dt = 2πr (dr/dt)
dr/dt = (dA/dt)/(2πr)
dr/dt = π/(2π*2)
dr/dt = 0.25 cm/min

Hope this helps.
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The directrix is y=7.

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