Question

A medicine capsule is in shape of a cylinder with two hemispheres stuck to each of its ends .length of capsule is 15mm and width is 5mm find volume of the capsule

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Answer 1

Answer:

220 mm

Step-by-step explanation:

Given:

Length of Capsule (l) = 14 mm

Diameter of Capsule = Diameter of Cylinder =5 mm

Radius = 2

Diameter

Therefore, Radius of each Hemisphere = Radius of Cylinder = r =

25

= 2.5 mm

Length of Cylinder = AB = Total length of Capsule - Radius of left Hemisphere - Radius of Right Hemisphere

=14−2.5−2.5=9 mm

Surface Area of Capsule = Curved Surface Area of Cylinder + Surface Area of Left Hemisphere + Surface Area of Right Hemisphere

=2πrl+2πr

2

+2πr

2

=2πrl+4πr

2

=2×

7

22

×2.5×9+4×

7

22

×2.5

2

=

7

22

[45+25]=

7

22×70=220 mm

2

Answer 2

Given :

• Length of the Capsule = 15mm
• Width of the Capsule = 5mm

To Find :

• Volume of the capsule

Solution :

As per the question,

• A medicine capsule is in shape of a cylinder with two hemispheres stuck to each of its ends.

★ CSA of cylinder :

Now we have to find the radius

So, Diameter of Cylinder = 5mm

→ Radius of Cylinder = Diameter / 2

→ Radius of Cylinder = 5 / 2

So, Diameter of Hemisphere = 5mm

→ Radius of Hemisphere = Diameter / 2

→ Radius of Hemisphere = 5 / 2

Now we have to find the height of the cylinder.

⇒ Height of the Cylinder = Length of the Capsule - 2 × Radius of Hemisphere

⇒ Height of the Cylinder = 14 - 2 × 5/2

⇒ Height of the Cylinder = 14 - 5

⇒ Height of the Cylinder = 9mm

By using formula,

We have π = 22/7 , r = 5/2 , h = 9

⇒ CSA of cylinder = 2πrh

⇒ CSA of cylinder = 2 × 22/7 × 5/2 × 9

⇒ CSA of cylinder = 22 × 45 / 7

⇒ CSA of cylinder = 990 / 7 mm²

★ CSA of Hemisphere :

We have π = 22/7 , r = 5/2

⇒ CSA of Hemisphere = 2πr²

⇒ CSA of Hemisphere = 2 × 22/7 × (5/2)²

⇒ CSA of Hemisphere = 2 × 22/7 × 5×5/2×2

⇒ CSA of Hemisphere = 2 × 22/7 × 25/4

⇒ CSA of Hemisphere = 11 × 25 / 7

⇒ CSA of Hemisphere = 275 / 7mm²

Now we have to find the CSA of two Hemispheres.

★ CSA of 2 Hemispheres :

We Know that, CSA of Hemisphere = 275 / 7mm²

⇒ CSA of 2 Hemisphere = 2 × CSA of Hemisphere

⇒ CSA of 2 Hemisphere = 2 × 275/7

⇒ CSA of 2 Hemisphere = 550/7mm²

★ Total area of the Capsule :

We know that, CSA of cylinder = 990/7 , CSA of 2 Hemisphere = 550/7

⇒ Total area of the Capsule = CSA of cylinder + CSA of 2 Hemisphere

⇒ Total area of the Capsule = 990/7 + 550/7

⇒ Total area of the Capsule = 990 + 550 / 7

⇒ Total area of the Capsule = 1540 / 7

⇒ Total area of the Capsule = 220mm²

•°• Total area of the Capsule = 220mm²