2005
Mathematics
JAMB
The radius r of a circular disc is increasing at the rate of 0.5cm/sec. At what rate is the area of the disc increasing when its radius is 6cm?
A.
36 π cm2/sec
B.
18 π cm2/sec
C.
6 π cm2/sec
D.
3 π cm2/sec
Correct Answer: 6 π cm2/sec
Explanation
Increase in radius dr/dt = 0.5 Area of the circular disc = πr2 Increase in area: dA/dr = 2πr Rate of increase in area: dA/dt = dA/dr * dr/dt when r = 6cm = 2πr * 0.5 = 2 * π * 6 * 0.5 2 * π * 6 * 1/2 = 6 π cm2/sec
Increase in radius dr/dt = 0.5 Area of the circular disc = πr2 Increase in area: dA/dr = 2πr Rate of increase in area: dA/dt = dA/dr * dr/dt when r = 6cm = 2πr * 0.5 = 2 * π * 6 * 0.5 2 * π * 6 * 1/2 = 6 π cm2/secTHIS WEEK's
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