A medicine capsule is in the shape of a cylinder with two hemi

Q) 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.

Ans:

We reconstruct the diagram of capsule as combination of a cylinder with two hemispheres at both ends.

Let’s calculate dimensions of this cylinder and hemispheres.

Since the diameter of hemisphere is 5 mm, hence its radius will be 2.5 mm

Same will also be the radius of the cylinder.

Now, the length of the cylinder = 14 – 5 = 9 mm

Let’s calculate surface area of each shape one by one:

(i) Surface Area of cylindrical shape:

We know that the curved surface area of the cylinder = $2 \pi r h$

Given that the radius of the cylinder is 2.5 mm and height of the cylinder is 9 mm

$\therefore$ the surface area of the cylinder = $2 \pi (2.5) (9) = 45 \pi$

(ii) Surface area of Hemispheres:

We know that, surface area of a hemisphere = $2 \pi r^2$

Since, the radius of the hemisphere = 2.5 mm

$\therefore$ the surface area of a hemisphere = $2 \pi (2.5)^2 = 12.5 \pi$

$\therefore$ the surface area of two hemispheres = $2 \times 12.5 \pi = 25 \pi$

(iii) Total Surface Area of Capsule:

$\since$ the surface area of the entire capsule = Surface area of Cylinder + Surface Area of 2 hemispheres

= $45 \pi + 25 \ pi = 70 \pi$

= $70 \times \frac{22}{7} = 220$

Therefore, Surface Area of the Capsule is 220 mm²

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