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JAMB Mathematics 2019 Paper

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Question : 48

Total: 73

If the volume of a frustrum is given as

V = \frac{\pi h}{3}(R^2 + Rr + r^2)

\frac{dV}{dR}

.

$\frac{\pi h}{3}(2R + r)$
$2R + r + \frac{\pi h}{3}$
$\frac{\pi h}{3}(2R^2 + r + 2r)$
$\frac{2R^2}{3}\pi h$

Solution:

$V = \frac{\pi h}{3}(R^2 + Rr + r^2)$

$V = \frac{\pi R^2 h}{3} + \frac{\pi R r h}{3} + \frac{\pi r^2 h}{3}$

$\frac{dV}{dR} = \frac{2\pi R h}{3} + \frac{\pi r h}{3}$

= $\frac{\pi}{3}(2R + r)$

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