medicine capsule is in shape of a cylinder with two hemispheres stuck to each of its ends .length of capsule is 14mm and width is 5mm find surface area
Answers
Answer:
220 m²
Step-by-step explanation:
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A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 13.10). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends
Solution:
As the capsule is in the shape of a cylinder with 2 hemispheres stuck to its ends, the diameter of the capsule is equal to the diameter of its cylindrical part and the diameter of its hemispherical part.
From Fig. 13.10, it’s clear that the capsule has the curved surface of two hemispheres and the curved surface of a cylinder.
Surface area of the capsule = 2 × CSA of hemispherical part + CSA of cylindrical part
The surface area of the capsule can be found by using formulae;
CSA of the hemisphere = 2πr2, where r is the radius of the hemisphere
CSA of the cylinder = 2πrh, where r and h are the radius and height of the cylinder respectively.
Diameter of the capsule, d = 5 mm
Radius of the hemisphere, r = d/2 = 5/2 mm
Radius of the cylinder, r = 5/2 mm
Length of the cylinder = Length of the capsule - 2 × radius of the hemisphere
h = 14 mm - 2 × 5/2 mm = 9 mm
Surface area of the capsule = 2 × CSA of hemispherical part + CSA of cylindrical part
= 2 × 2πr2 + 2πrh
= 2πr (2r + h)
= [2 × 22/7 × 5/2 mm × (2 × 5/2 mm + 9 mm)]
= 110/7 mm × 14 mm
= 220 mm2
Thus, the surface area of the capsule is 220 mm2.