Question

A medicine capsule as shown in the figure us in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is $$12\ mm$$, and the diameter of the capsule is $$5\ mm$$. Find its surface area.

Answer 1

Given:
Diameter of cylinder $$=5\ mm$$
Radius of cylinder $$=\dfrac {Diameter}{2}=\dfrac 52\ mm$$
Height of cylinder $$=12-5=7\ mm$$
Here, Diameter of hemisphere $$=5\ mm$$
So, Radius of Hemisphere $$=\dfrac{Diameter}{2}=\dfrac 52\ mm$$
Total area of the capsule = CSA of cylinder +CSA of $$2$$ hemispheres
$$=2\pi rh +2\times 2\pi r^2$$
$$=2\times \dfrac{22}{7}\times \dfrac 52 \times 7+4\times \dfrac{22}{7}\times \dfrac 52\times \dfrac 52$$
$$=\dfrac {22}{7} (35+25)$$
$$=\dfrac {22}{7}\times 60$$
$$=188\dfrac {4}{7}\ sq. mm$$