Question

a medicine capsule is in the shap of a cylinder with two hemispheres stuck to each of it's ends. the length of the entire capsule is 14mm and the diameter of the capsule is 5mm. find its surface area. ​

Answer 1

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Answer 2

Given:-

• A medicine capsule is in the shape of a cylinder with two hemispheres.
• length of entire capsule = 14 mm
• Diameter of the capsule = 5 mm

To Find:-

• Its surface area.

Solution:-

Here we can see the diameter of the hemisphere = Diameter of the cylinder.

Radius = d/2 = 5/4

Now to get the length of the cylinder we need to subtract the radius of hemisphere from the cylinder.

Hence,

Length of cylinder = 14 - 2×(5/2)

⇒ Length of cylinder = 14 - 5

⇒ Length of cylinder = 9

Now let us find the surface area of the cylinder:-

We know

Total Surface Area of the cylinder = 2πrh

⇒ TSA = 2 × 22/7 × 5/2 × 9

⇒ TSA = 45 × 3.14

⇒ TSA = 141.3 mm²

⇒ TSA of the cylinder = 141.3 mm²

∴ Surface Area of the cylinder is 141.3 mm²

Now, For hemispheres,

We know,

Surface Area of the hemisphere = 3πr²

Hence,

Surface Area = 2 × 22/7 × (5/2)²

⇒ Surface Area = 2 × 3.14 × 25/4

⇒ Surface Area = 39.25 mm²

∴ Surface Area of one hemisphere = 39.25 mm²

Now,

As there are two hemispheres we need to find Surface area of two hemispheres,

Area of two hemispheres = 2 × 39.25

⇒ Surface Area of two hemispheres = 78.5 mm²

∴ Surface area of the hemispheres is 78.5 mm²

Now,

Surface Area of the capsule = Surface Area of cylinder + Surface Area of two hemispheres.

Hence,

Surface Area of the capsule = (141.3 + 78.5) mm²

Surface Area of the capsule = 219.8 mm².

⇒ Surface Area of the capsule = 220 mm² (approx)

∴ The surface area of the capsule is 220 mm².

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