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.

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

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.

✠Given

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends

Length of the entire capsule = 14 mm

Diameter of the capsule = 5 mm

✠To Find

Total Surface Area of Capsule

✠Answer

Total Surface Area of Capsule is 220 mm²

✠Calculations

First we need to know about some basic terms before going into answer

Diameter : The diameter is the length of the line through the center that touches two points on the edge of the circle.

Radius : The distance from the center of the circle to any point on the circle

Also :

Diameter = 2 × Radius

Radius = Diameter/2

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Total Area of the Capsule

= Curved Surface Area of Cylinder + Curved Surface Area of 2 Hemispheres

= Curved Surface Area of Cylinder + 2 × (Curved Surface Area of Hemisphere)

= 2πrh + 2 × (2πr²)

= 2 × π × r × h + 2 × (2 × π × r²)

Since radius = diameter/2

= 2 × π × (diameter/2) × h + 2 × [2 × π × (diameter/2)²]

= 2 × π × (5mm/2) × h + 2 × [2 × π × (5mm/2)²]

= 2 × π × (5mm/2) × h + 2 × [2 × π × ((5mm × 5mm)/(2 × 2))]

Since π = 22/7

= 2 × 22/7 × (5mm/2) × h + 2 × [2 × 22/7 × ((5mm × 5mm)/(2 × 2))]

= 2 × 22/7 × (5mm/2) × h + 2 × [2 × 22/7 × ((5mm²)/(2)²)]

= 2 × 22/7 × (5mm/2) × h + 2 × [(2 × 22 × 5² mm²) /7 × 2²]

= 2 × 22/7 × (5mm/2) × h + 2 × [(44 × 5² mm²)/7 × 2²]

= 2 × 22/7 × (5mm/2) × h + 2 × [(11 × 2² × 5² mm²)/7 × 2²]

= 2 × 22/7 × (5mm/2) × h + 2 × [(11 × 5² mm²)/7]

= 2 × 22/7 × (5mm/2) × h + 2 × [(275 mm²)/7]

= 2 × 22/7 × (5mm/2) × h + [2 × (275 mm²)/7]

= 2 × 22/7 × (5mm/2) × h + [550 mm²)/7]

= 44/7 × (5mm/2) × h + [550 mm²)/7]

= (44 × 5mm)/(7 × 2) × h + [550 mm²)/7]

= (220 mm)/(14) × h + [550 mm²)/7]

= 15.714 mm × h + [550 mm²)/7]

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We need find "h" now :

Height of Cylinder + 2 × Radius of Hemisphere = Length of entire capsule

⇒ Height of Cylinder + 2 × Radius of Hemisphere = 14 mm

⇒ Height of Cylinder + 2 × (5 mm/2) = 14 mm

⇒ Height of Cylinder + 1 × (5 mm/1) = 14 mm

⇒ Height of Cylinder + 5 mm = 14 mm

⇒ Height of Cylinder + 5 mm - 5mm = 14 mm - 5mm

⇒ Height of Cylinder = 9mm

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= 15.714 mm × 9 mm + [550 mm²)/7]

= 141.426 mm² + 78.571 mm²

= 141.426 mm² + 78.571 mm²

= 219.997 mm²

= 220 mm² (Approximately)

∴ Total Surface Area of Capsule is 220 mm²

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