a metal pipe is 77 cm long, the inner diameter of the cross- section is 4 cm and the outer diameter is 4.4cm. find the 1. inner curved surface area2. outer curved surface area3. total surface area
Answers
Answer:
Inner Surface area of the Pipe = 968 Square cm.
Outer Surface area of the pipe = 1064.8 Square cm.
Total Surface Area = = 2038.08 Square cm.
Step-by-step explanation:
A pipe will have two layers as shown in picture.
There is a inner Cylinder and Outer Cylinder.
Inner Radius = Inner Diameter / 2 = 4 / 2 = 2 cm = r
Outer Radius = Outer Diameter / 2 = 4.4/2 = 2.2 cm = R
Height of the pipe = 77 cm = h
Inner Surface area of the Pipe = 2∏rh = 2*22*2*77/7 = 968 Square cm.
Outer Surface area of the pipe = 2∏Rh = 2*22*2.2*77/7 = 1064.8 Square cm.
Total Surface area = Inner Surface area + Outer Surface area + 2 * Cross section surface area.
The cross section suface area is present at two ends of the pipe.
This is the area covered between 2 circles.
Total Surface area = Inner Surface area + Outer Surface area + 2 * Cross section surface area.
= 968 + 1064.8 + 2*∏(R^2 – r^2)
= 2032.8 + 2*22*(2.2*2.2 – 2*2)/7
= 2032.8 + 5.28
= 2038.08 Square cm.
Step-by-step explanation:
i) Inner curved surface area = 2πrh
= 2 × 22/7 × 2 cm × 77 cm
= 968 cm²
ii) Outer curved surface area = 2πRh
= 2 × 22/7 × 2.2 cm × 77 cm
= 1064.8 cm²
iii) The total surface area of the pipe can be obtained by adding the inner and outer curved surface areas along with the area of both the circular ends.
We can find the area of circular ends by subtracting the area of the inner circle from the outer circle area.
Area of both the circular ends of the pipe = 2 π (R² - r²)
TSA of pipe = CSA of inner surface + CSA of outer surface + Area of both the circular ends of the pipe
Hence, TSA of the pipe = 2πrh + 2πRh + 2π(R² - r²)
Now, area of both the circular ends of the pipe = 2π(R² - r²)
= 2 × 22/7 × [(2.2 cm)² - (2 cm)²]
= 2 × 22/7 × [4.84 cm² - 4 cm²]
= 2 × 22/7 × 0.84 cm²
= 5.28 cm²
Total surface area = 2πrh + 2πRh + 2π (R² - r²)
= 968 cm² + 1064.8 cm² + 5.28 cm² [Since, Inner curved surface area = 968 cm², Outer curved surface area = 1064.8 cm²]
= 2038.08 cm²