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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
A = \(\pi\)r2, \(\frac{\delta A}{\delta r}\) = 2πr
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
Source: Myschool Past Questions Archive (Record #27084)