JAMB 1992 · UME · Q40

Calculus (JAMB bridge)

A student blows a balloon and its volume increases at a rate of $\pi(20 - t^2)\text{ cm}^3\text{s}^{-1}$ after $t$ seconds. If the initial volume is $0\text{ cm}^3$ , find the volume of the balloon after 2 seconds.

Worked solution (try it first)

Integrate the rate to get the volume: $V = \pi\left(20t - \frac{t^3}{3}\right) + c$ .
The volume is 0 when $t = 0$ , so $c = 0$ .
At $t = 2$ : $V = \pi\left(40 - \frac83\right)$
$\approx 37.33\pi\text{ cm}^3$ , option B.

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