NCERT Exemplar Solutions Class 10 Mathematics Solutions for Surface Areas and Volumes - Exercise 12.1 in Chapter 12 - Surface Areas and Volumes
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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 to its ends. The length of entire capsule is 2 cm. The capacity of the capsule is
Capsule consists of 2 Hemispheres and a Cylinder
r=\frac{0.5}{2} \mathrm{~cm}=0.25 \mathrm{~cm} \\ \Rightarrow \mathrm{r}=0.25 \mathrm{~cm}
Total length of capsule = r + h + r
⇒ 2 cm = 2r + h
⇒ 2 = 2 × 0.25 + h
⇒ h = 2 – 0.5 = 1.5 cm
Volume of capsule = Vol. of two hemispheres + Vol. of cylinder
=2 \times\left(\frac{4}{3} \pi r^{3} \times \frac{1}{2}\right)+\pi r^{2} h=\frac{4}{3} \pi r^{3}+\pi r^{2} h \\ =\pi r^{2}\left[\frac{4}{3} r+h\right]=\frac{22}{7} \times 0.25 \times 0.25\left[\frac{4}{3} \times 0.25+\frac{15}{10}\right] \\ =\frac{22}{7} \times 0.25 \times 0.25\left[\frac{4}{3} \times \frac{25}{100}+\frac{3}{2}\right] \\ =\frac{22}{7} \times 0.25 \times 0.25\left[\frac{1}{3}+\frac{3}{2}\right] \\ =\frac{22}{7} \times 0.25 \times 0.25\left[\frac{2+9}{6}\right] \\ =\frac{22 \times 25 \times 25 \times 11}{7 \times 6 \times 100 \times 100}=\frac{121}{42 \times 8}=\frac{121}{336}
∴ Volume of capsule = \frac{121}{336}cm^3
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