A capsule

A medicine capsule is a cylinder with two hemispheres stuck to each end. Its length is 14 mm, and its diameter is 5 mm. Find its surface area.

Correct answer:

A =  219.9 mm²

Step-by-step explanation:

$$\begin{gathered} h=14\text{mm} \\ d=5\text{mm} \\ r=d/2=5/2=\frac{5}{2}=2.5\text{mm} \\ l=h-2\cdot r=14-2\cdot 2.5=9\text{mm} \\ {S}_1=4\pi \cdot r^2=4\cdot 3.1416\cdot 2.5^2\doteq 78.5398{\text{mm}}^2 \\ {S}_2=\pi \cdot d\cdot l=3.1416\cdot 5\cdot 9\doteq 141.3717{\text{mm}}^2 \\ A=S_1+S_2=78.5398+141.3717=219.9{\text{mm}}^2 \end{gathered}$$

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