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A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is $20$ cm and the diameter of the cylinder is $7$ cm. Find the total volume of the solid. (Use $\pi = \frac{22}{7}$)
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Radius of cylinder = radius of hemisphere $= \frac{7}{2}$ cm (1/2 Mark)
Total height of solid $= 20$ cm
Height of cylinder $= (20 - \frac{7}{2} - \frac{7}{2})$ cm $= 13$ cm (1/2 Mark)
Total volume of solid $= [\frac{22}{7} \times (\frac{7}{2})^2 \times 13 + 2 \times \frac{2}{3} \times \frac{22}{7} \times (\frac{7}{2})^3]$ (1 Mark)
$= \frac{22}{7} \times (\frac{7}{2})^2 \times (13 + \frac{14}{3})$ (1 Mark)
$= \frac{4081}{6} = 680.1$ cm$^3$ (approx.) (1 Mark)
Total height of solid $= 20$ cm
Height of cylinder $= (20 - \frac{7}{2} - \frac{7}{2})$ cm $= 13$ cm (1/2 Mark)
Total volume of solid $= [\frac{22}{7} \times (\frac{7}{2})^2 \times 13 + 2 \times \frac{2}{3} \times \frac{22}{7} \times (\frac{7}{2})^3]$ (1 Mark)
$= \frac{22}{7} \times (\frac{7}{2})^2 \times (13 + \frac{14}{3})$ (1 Mark)
$= \frac{4081}{6} = 680.1$ cm$^3$ (approx.) (1 Mark)