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State true or false.

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. Its surface area will be $220 mm 2$ .

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True

False

answer is A.

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Detailed Solution

Given,
The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm.
We have to check if the surface area will be

220 mm 2

.
Using the formula,

(r) = diameter 2

Constructing the required diagram:
Question Image

∴ r = 52 mm

Understand that, the height of the cylinder:

∴ h = 14 − 2 × 52 ⇒ h = 9 mm

Note that,
Curved surface area of cylinder

= 2 π r h

Curved surface area of hemisphere

= 2 π r 2

Total surface area of the capsule = Curved surface area of cylinder

+ 2 x

curved surface area of a hemisphere.

∴ Total surface area of the capsule = 2 π r h + 2 × 2 π r 2 ⇒ Total surface area of the capsule = 2 π r (h + 2 r) = 2 × 227 × 52 × 9 + 2 × 52 = 227 × 5 × (9 + 5)

Simplifying further,

⇒ Total surface area of the capsule = 227 × 5 × 14 = 220 mm 2

So, the surface area of the medicine capsule is

220 mm 2

and thus the statement is true.
Therefore, option 1 is correct.

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