Question

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends .The length of the entire capsule is 14 mm and the diameter of the capsule is 7 mm. find its volume​

Answer 1

$\large{\underline{\rm{\red{\bf{Question:-}}}}}$

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

$\large{\underline{\rm{\red{\bf{Given:-}}}}}$

The diameter of the capsule = 5 mm

The entire length of the capsule = 14 mm

$\large{\underline{\rm{\red{\bf{To \: Find:-}}}}}$

The volume of the medicine capsule.

$\large{\underline{\rm{\red{\bf{Solution:-}}}}}$

Here, given the diameter of the capsule = 5 mm

∴ Radius = $\sf \dfrac{5}{2} =2.5 \: mm$

Now, the length of the capsule = 14 mm

So, the length of the cylinder = $\sf 14-(2.5+2.5) = 9 \: mm$

The surface area of a hemisphere = $\sf 2 \pi r^{2}$

Substituting their values,

$\implies \sf 2 \times \dfrac{22}{7} \times 2.5 \times 2.5$

$\sf =\dfrac{275}{7} \: mm^{2}$

Now, the surface area of the cylinder = $\sf 2 \pi r h$

$\sf \implies 2 \times \dfrac{22}{7} \times 2.5 \times 9$

$\sf \dfrac{22}{7} \times 45 =\dfrac{990}{7} \: mm^{2}$

Thus, the required surface area of medicine capsule will be  = 2 × Surface area of hemisphere + Surface area of the cylinder

$\sf \implies 2 \times \dfrac{275}{7} \times \dfrac{990}{7}$

$\sf \implies \dfrac{550}{7} +\dfrac{990}{7} =\dfrac{1540}{7}$

$\sf \implies \underline{\underline{220 \: mm^{2}}}$

Therefore, the required surface area of medicine capsule is 220 mm²