Question

A cylindrical metal pipe of thickness 1.4 cm and external diameter 56 cm is
14 m long. Find the volume of metal used in the construction of the pipe.
​

Answer 1

Given :

• Thickness of a cylindrical metal pipe = 1.4 cm
• External diameter of the cylindrical metal pipe = 56 cm
• Length of the metal pipe = 14 m

To find :

• Volume of metal used in the construction of the pipe

Solution :

Here, firstly we will convert the length of the metal pipe from m into cm. Because while doing calculation all the units should be same to get the correct answer.

As we know,

• 1 m = 100 cm

To convert the value from m into cm, mutlitply it by 100.

➪ Length of the metal pipe = 14 m

➪ Length = 14 × 100 = 1400

∴ Length of the metal pipe = 1400 cm

Now, we will calculate the external radius of the metal pipe.

➳ Formula to calculate radius, when diameter is given :-

• Radius = Diameter ÷ 2

Substituting the given values, we get :-

➪ External radius of the metal pipe = 56 ÷ 2

➪ External radius of the metal pipe = 28

∴ External radius of the metal pipe = 28 cm

Now, we will find the volume of the external metal pipe :-

➳ Formula to calculate volume of metal pipe, when radius and length is given :-

• Volume of metal pipe = πr²l

where,

• Take π = 22/7
• r = radius of the metal pipe
• l = length of the metal pipe

Substituting the given values, we get :-

➪ External volume = 22/7 × (28)² × 1400

➪ External volume = 22/7 × 28 × 28 × 1400

➪ External volume = 22 × 4 × 28 × 1400

➪ External volume = 3,449,600

∴ External volume of the metal pipe = 3,449,600 cm³

Now, we will find the internal radius of the metal cylinder.

To find the radius of the metal cylinder subtract (1.4 + 1.4) cm from the external radius of the metal pipe.

➪ Internal radius = 28 - (1.4 + 1.4) = 28 - 2.8 = 25.2

∴ Internal radius of the metal pipe = 25.2 cm

Now, calculate the internal volume of the metal pipe.

Using formula,

• Volume of metal pipe = πr²l

Substituting the given values, we get :-

➪ Internal volume = 22/7 × (25.2)² × 1400

➪ Internal volume = 22/7 × 25.2 × 25.2 × 1400

➪ Internal volume = 22/7 × 3.6 × 25.2 × 1400

➪ Internal volume = 399,168

∴ Internal volume of the metal pipe = 399,168 cm³

To find the volume of the metal pipe used in the construction of the pipe, subtract the internal volume of the metal pipe from the external volume of the metal pipe.

➪ Volume of metal used = 3,449,600 - 399,168

➪ Volume of metal used = 3,050,432

Therefore,

• Volume of metal used in the construction of the pipe = 3,050,432 cm³