Question

A medicine capsule is in the Shape of a cylinder with two hemispheres stuck to each of its nds The length of entire Capsule is limm. and Find ids the diameter of the Capsule is 5mm. Surface area​

Answer 1

Answer:

• Surface area of capsule = 220mm^2

Step-by-step explanation:

Correct question:

A medicine capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. The length of the entire capsule is 14mm and the diameter of the capsule is 5mm. Find its surface area.

Given:

• Medicine capsule is in the shape of cylinder.
• It has two hemispherical ends.
• Height of entire capsule = 14mm
• Diameter of capsule = 5mm

To find:

• Total surface area of the capsule.

Solution:

Since, diameter of the capsule is 5mm, radius of the capsule will be:

⟶ r = d/2

⟶ r = 5/2

⟶ r = 2.5mm

Let us find the height of the cylinder. According to the question, we know that:

⟶ Height of cylinder = Total height of capsule - 2×Radius of hemisphere

⟶ Height of cylinder = 14mm-(2×2.5)mm

⟶ Height of cylinder = 14mm-5mm

⟶ Height of cylinder = 9mm

Now, let us find the Curved Surface Area of cylinder. We know that:

⟶ CSA of cylinder = 2πrh

⟶ CSA of cylinder = 2×22/7×2.5×9

⟶ CSA of cylinder = 2×22/7×2.5×9

⟶ CSA of cylinder = 990/7

⟶ CSA of cylinder = 141.42mm^2

Further, let us find the Curved Surface Area of hemisphere. We know that:

⟶ CSA of hemisphere = 2πr^2

⟶ CSA of hemisphere = 2×22/7×2.5×2.5

⟶ CSA of hemisphere = 2×22/7×6.25

⟶ CSA of hemisphere = 275/7

⟶ CSA of hemisphere = 39.28mm^2

Finally,

⟶ TSA of capsule = CSA of cylinder + 2×CSA of hemisphere

⟶ TSA of capsule = 141.42 + 2×39.28

⟶ TSA of capsule = 141.42 + 78.56

⟶ TSA of capsule = 219.98mm^2

⟶ TSA of capsule = 220mm^2(approx.)

Hence, the surface area of capsule is 220mm^2

Answer 2

Given:-

• The shape of the capsule = 2 hemisphere + 1 cylinder
• Length of the capsule = 14 mm
• Width of the capsule = 5 mm

To Find:-

• The total surface area of the given capsule.

Solution:-

• ⟶ The base diameter of the hemispheres = 5 mm

• ⟶ The radius of the hemispheres = 5/2 = 2.5 mm

• ⟶The height of the hemisphere = 2.5 mm

• ⟶The total height of the hemispheres = 2.5×2 = 5 mm

The height of cylinder = 14-5 = 9 mm

• ⟶ Surface area of cylinder = 2 × 22/7 × 2.5 × 9 = 141.42 mm²
• ⟶Curved surface area of one hemisphere = 2 × 22/7 × (2.5)² = 2×22/7×6.25 = 39.28 mm²

• ⟶CSA of two hemispheres = 39.28 × 2 = 78.56 mm²

• ⟶Total surface area = 141.42 + 78.56 = 219.98 mm²

The approximate surface area of the capsule is 219.98 mm².