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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 (A) 0.36 cm^3

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

(A) 0.36 cm3               (B) 0.35 cm3                (C) 0.34 cm3                (D) 0.33 cm3

Answers (1)

 

            Diameter of hemisphere = 0.5 cm

        Radius =\frac{0.5}{2}=\frac{5}{20}=\frac{1}{4}=0.25cm

       \text{ Volume of hemisphere }=\frac{2}{3}\pi r^{3}

                        = \frac{2}{3}\times\frac{22}{7}\times \frac{1}{4}\times\frac{1}{4}\times \frac{1}{4}=\frac{11}{336}

        \text{ Volume of two hemispheres} =\frac{2 \times11}{336} =\frac{11}{168}

            Similarly radius of cylinder = 0.25

            Height  = 2- 0.25 -0.25

                        = 2- 0.5

                        =1.5 cm

        Volume = \pi r ^{2}h

                        = \frac{22}{7}\times \frac{1}{4}\times\frac{1}{4}\times\frac{15}{10}\Rightarrow \frac{33}{112}

            The total volume of capsule = volume of two hemispheres + volume of the cylinder

                        =\frac{11}{168}+\frac{33}{112}

                        =0.065 +0.294

                        = 0.359cm3

                        =0.36cm3   (approximate)

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