A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is ______.

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A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is 0.36 cm3. Explanation: Given, Diameter of cylinder = Diameter of hemisphere = 0.5 cm ...[Since, both hemispheres are attach with cylinder] $\therefore$ Radius of cylinder (r) = Radius of hemisphere (r) = 0.$\frac{5}{2}$ = 0.25 cm ...[∵ Diameter = 2 $\times$ radius] And total length of capsule = 2 cm $\therefore$ Length of cylindrical part of capsule, h = Length of capsule – Radius of both hemispheres = 2 – (0.25 + 0.25) = 1.5 cm Now, capacity of capsule = Volume of cylinder part + 2 $\times$ Volume of hemisphere = `pi"r"^2"h" + 2 xx $\frac{2}{3}$ pi"r"^3` ...[∵ Volume of cylinder = $\pi$ $\times$ (radius)2 $\times$ height and volume of hemisphere = $\frac{2}{3}$ $\pi$(radius)3] = `$\frac{22}{7}$ [(0.25)^2 xx 1.5 + $\frac{4}{3}$ xx (0.25)^3] = $\frac{22}{7}$ [0.09375 + 0.0208] = $\frac{22}{7}$ xx 0.11455` = 0.36 cm3 Hence, the capacity of capsule is 0.36 cm3. [Solution diagram: 268818_solution_1.png]

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