Calculate the total surface area of a pipe with inner surface area 1508.5 square cm, outer surface area 2514.2 square cm, and inner radius 3 cm and outer radius 5 cm. *

The total surface area of the pipe is 4123.31 cm²

Step-by-step explanation:

Total surface area (TSA) of a pipe is calculated as;

Outer area of the pipe + Inner area of the pipe + cross section of the two ends

TSA = 2πRL + 2πrL + 2π(R² - r²)

TSA = 2π(RL + rL + R² - r²)

where;

R is the outer radius

r is the inner radius

L is length of the pipe

Determine the length of the pipe

Outer surface area of the pipe is  calculated as;

outer surface of the pipe = 2πRL

2514.2  = 2πRL

2514.2 = (2π x 5) L

2514.2 = 31.42 L

L = 2514.2 / 31.42

L = 80.02 cm

Finally, determine the total surface area of the pipe

TSA = 2π(RL + rL + R² - r²)

TSA = 2π(5x80.02 + 3x80.02 + 5² - 3²)

TSA =  2π(400.1 + 240.06 + 16)

TSA =  2π(656.16)

TSA = 4123.31 cm²

Therefore, the total surface area of the pipe is 4123.31 cm²

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