Question on: JAMB Mathematics - 2013
The radius of a circle is increasing at the rate of 0.02cms-1. Find the rate at which the area is increasing when the radius of the circle is 7cm.
A
0.75cm2S-1
B
0.53cm2S-1
C
0.35cm2S-1
D
0.88cm2S-1
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Correct Option: D
A = \(\pi\)r2, \(\frac{\delta A}{\delta r}\) = 2Ï€r
So, using \(\frac{\delta A}{\delta t}\) = \(\frac {\delta A}{\delta r}\) x \(\frac {\delta A}{\delta t}\)
= 2\(\pi\)r x 0.02
= 2\(\pi\) x 7 x 0.02
= 2 x \(\frac{22}{7}\) x 0.02
= 0.88cm2s-1
So, using \(\frac{\delta A}{\delta t}\) = \(\frac {\delta A}{\delta r}\) x \(\frac {\delta A}{\delta t}\)
= 2\(\pi\)r x 0.02
= 2\(\pi\) x 7 x 0.02
= 2 x \(\frac{22}{7}\) x 0.02
= 0.88cm2s-1
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