2023
Mathematics
JAMB
The area A of a circle is increasing at a constant rate of 1.5 cm 2s−1 . Find, to 3 significant figures, the rate at which the radius r of the circle is increasing when the area of the circle is 2 cm2 .
A.
0.200 cms−1
B.
0.798 cms−1
C.
0.300 cms−1
D.
0.299 cms−1
Correct Answer: 0.299 cms−1
Explanation
Area of a circle (A) = πr2 Given dA/dt=1.5 cm2s-1 dr/dt = ? A = 2cm2 Now 2 = πr 2 = r2 = 2/π r = √(2/π) cm = 0.798cm dr/dt = dA/dt × dr/dt dA/dr= 2πr (differentiating A = πr2) dr/dA=1/2πr dr/dt=1.5 × 1/(2 × π × 0.798) = 1.5 × 0.199 dr/dt = 0.299cms−1 (to 3 s.f)
Area of a circle (A) = πr2 Given dA/dt=1.5 cm2s-1 dr/dt = ? A = 2cm2 Now 2 = πr 2 = r2 = 2/π r = √(2/π) cm = 0.798cm dr/dt = dA/dt × dr/dt dA/dr= 2πr (differentiating A = πr2) dr/dA=1/2πr dr/dt=1.5 × 1/(2 × π × 0.798) = 1.5 × 0.199 dr/dt = 0.299cms−1 (to 3 s.f)THIS WEEK's
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