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

$\underline{\underline{\sf{\maltese\:\:Question}}}$

• 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.

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• 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

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• Total Surface Area of Capsule

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

• Total Surface Area of Capsule is 220 mm²  

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

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

__________________________________

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]

________________________________

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

________________________________

= 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  

________________________________

Request :

If there is any difficulty viewing this answer in app, Kindly see this answer at Web (https://brainly.in/) for clear steps and understanding.

See the answer at :

brainly.in/question/30004506

Answer 2

Answer:

Given,

length of capsule (l) = diameter of cylinder = 5mm

Radius = Daimeter/2

Therefore, Radius of each hemisphere = Radius of cylinder = r = 5/2 = 2.5mm

length of cylinder = AB = total length of cylinder - radius of left hemisphere - radius of right hemisphere

14 - 2.5 - 2.5 = 9mm

Surface area of capsule = curved surface area of cylinder + surface area of length hemisphere + surface area of right hemisphere

2πrl + 2πr² + 2πr²

2πrl + 4πr²

2 × 22/7 × 2.5 × 9 + 4 × 22/7 × 2.5²

22/7 [ 45 + 25 ]

22/7 × 70

220 mm²