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A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
"
Given:
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm.
To do:
We have to find its surface area.
Solution:
Diameter of each hemispherical end $=5 \mathrm{~mm}$
This implies,
Radius of each hemispherical end $=\frac{5}{2} \mathrm{~mm}$
Therefore,
Surface area of each hemispherical end $=2 \pi^{2}$
$=2 \times \frac{22}{7} \times \frac{5}{2} \times \frac{5}{2}$
$=\frac{275}{7} \mathrm{~mm}^{2}$
Surface area of both hemispherical ends $=\frac{2 \times 275}{7} \mathrm{~mm}^{2}$
$=\frac{550}{7} \mathrm{~mm}^{2}$
Total length of the capsule $=14 \mathrm{~mm}$
Length of the cylindrical surface $=$ Total length $-$ Radii of both hemispherical ends
$=14-2(\frac{5}{2})$
$=14-5$
$=9 \mathrm{~mm}$
Curved surface area of the cylindrical portion $=2 \pi r h$
$=2 \times \frac{22}{7} \times \frac{5}{2} \times 9$
$=\frac{990}{7} \mathrm{~mm}^{2}$
Total surface area of the capsule $=$ Area of both hemispherical ends $+$ Area of the cylindrical portion
$=\frac{550}{7}+\frac{990}{7}$
$=\frac{1540}{7} \mathrm{~mm}^{2}$
$=220 \mathrm{~mm}^{2}$.