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 4 mm, find its surface area. Also, find its volume.

Ans: 

Step 1: Let’s make  diagram for our better understanding of the question:

Given: Capsule length = 14 mm

Diameter of capsule = 4 mm

∴ Radius of capsule = = 2 mm

Step 2: Since the capsule is made of cylinder and 2 hemispheres at each end

∴ length of cylinder = length of capsule – 2 x radius of hemispheres

= 14 – 2 x 2 = 10 mm

Step 3: Surface area of the Capsule

= Surface area of Cylinder + 2 x Surface area of hemisphere

= 2 π R H + 2 x 2 π (R) ²

= 2 π (2) (10) + 4 π (2) ²

= 40 π + 16 π = 56 π

= 56 x   = 176 mm ²

Therefore, Surface Area of the capsule is 176 mm ² 

Step 4: Volume of the Capsule = Volume of Cylinder + 2 x Volume of hemispheres

= π R² H + 2 x π (R)³

= π (2)² (10) + x π x (2)³

= π 40 + x π = π

=  = 154.27 mm³

Therefore, Volume of the capsule is 154.27 mm³ 

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