The radius r of a circular disc is increasing at the rate of 0.5cm/sec. At...

JAMB 2005

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

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Correct Answer: Option C

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

There is an explanation video available below.

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The radius r of a circular disc is increasing at the rate of 0.5cm/sec. At...

Correct Answer: Option C

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