**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:**

**STEP BY STEP SOLUTION**

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 =

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

the surface area of the cylinder =

**(ii) Surface area of Hemispheres:**

We know that, surface area of a hemisphere =

Since, the radius of the hemisphere = 2.5 mm

the surface area of a hemisphere =

the surface area of two hemispheres =

**(iii) Total Surface Area of Capsule:**

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

=

=

**Therefore, Surface Area of the Capsule is 220 mm ^{2} **

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