A metal pipe is 77 cm long the inner diameter of the cross section is 4 cm and Outer diameter is 4.8 cm find inner curved surface area, outer curved area and total surface area
Answers
Inner radius(r) =2cm
Outer radius(R) =2.4cm
h=77cm
CSA= 2 pai (22/7) rh
=2 ✖ 22/7 ✖ 2 ✖ 77
=88 ✖ 11
=968 cm^2
HOPE IT HELPS....
Given :
- Height of pipe = 77cm
- Diameter of cross section = 4cm
- Outer diameter = 4.4cm
To Find :
Total surface area of the pipe.
Solution :
In the question, we are provided with the 3 things, the diameter of cross section, outer diameter and the height of pipe. So, first we will find the radius of both cross section and outer radius, by dividing the given Diameters by 2. After that first we will find the curved surface area of cross section then curved surface area of outer section, after that we will, after that we will further solve the question.
So -
First let's convert, the given diameters into radius -
4cm = 4/2
→ Inner Radius ,r = 2cm
4.4cm = 4.8/2
→ Outer Radius ,r '= 2.4cm
Now -
Let's find the CSA of cross section, by applying the formula of CSA of cylinder, which is -
2πrh = curved surface area of cylinder.
On substituting the values -
2 × 22/7 × 2cm × 77cm
2 × 22 × 2cm × 11cm
→ 968cm
Similarly -
Let's find the CSA of outer section, by applying the same formula again.
2 × 22/7 × 2.4cm × 77cm
2 × 22 × 2.4cm × 11cm
→ 1161.6cm
Now -
We will find the area of circle, by subtracting the base radius of Outer section, from the base radius of inner section.
→ π(r')² - πr²
→ 22/7 × (2.4)² - 22/7 × (2)²
[Taking 22/7 as Common]
→ 22/7 × [(2.4)² - (2)²]
→ 22/7 × [(5.76 - 4)]
→ 22/7 × 1.76
→ 5.5cm
At the end -
We will find the total surface area, by adding the CSA of inner cross section with outer section also with 2, and multiply it with the obtained base area -
→ TSA = 968cm + 1161.6cm + 2 × 5.5cm
→ TSA = 2140.6cm²
Therefore, the Total surface area of the pipe is 2140.6cm².