Ex 12.1, 6
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
Total area of the capsule
= Curved Surface area of cylinder
+ Curved Surface area of 2 hemispheres
Curved Surface area of cylinder
Diameter of cylinder = 5 mm
Radius of cylinder = (𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 )/2 = 𝟓/𝟐 mm
Here,
Diameter of hemisphere = 5mm
∴ Radius of hemisphere = (𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 )/2 = 𝟓/𝟐 mm
Now,
Height of cylinder + 2 × Radius of hemisphere = 14 mm
Height of cylinder = 14 – 2 × Radius of hemisphere
Height of cylinder = 14 – 2 × 5/2
Height of cylinder = 14 – 5
Height of cylinder = 9 mm
Now,
Curved surface Area of cylinder = 2𝜋rh
= 2×22/7×5/2×9
= (22 × 45)/7
= 𝟗𝟗𝟎/𝟕 mm2
Curved Surface area of hemisphere
Radius of hemisphere = 5/2 mm
Curved Surface Area of hemisphere = 2𝜋r2
= 2 ×22/7× (5/2)^2
= 2 ×22/7×(5 × 5)/(2 × 2)
= (11 × 5 × 5)/7
= 𝟐𝟕𝟓/𝟕 mm2
Thus,
Curved Surface area of 2 hemispheres = 2 × area of hemisphere
= 2 × 275/7
= 𝟓𝟓𝟎/𝟕 mm2
Now,
Total area of the capsule
= Curved Surface area of cylinder
+ Curved Surface area of 2 hemispheres
= 𝟗𝟗𝟎/𝟕+𝟓𝟓𝟎/𝟕
= (990 + 550)/7
= 1540/7
= 220 mm2
Hence, Total surface area of capsule is 220 mm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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