Two pipes with diameters of 9 and 12 cm need to be replaced with one with a cross-sectional

| September 7, 2021 | education

Two pipes with diameters of 9 and 12 cm need to be replaced with one with a cross-sectional area equal to the sum of the cross-sectional areas of the two given. What should be the diameter of the new pipe?

First, find the cross-sectional area of the first pipe. Let’s write the formula
S = P * R ^ 2. We have given the diameter, then we find the radius of the first pipe: R = d / 2 = 9/2 = 4.5 (cm)
Then the cross-sectional area of the first pipe will be: S1 = P * 4.5 ^ 2 = 20.25 P (cm ^ 2)
Find the radius and area of the second pipe. R = 12/2 = 6cm. Then the cross-sectional area of the second pipe will be: S2 = P * 6 ^ 2 = 36P (cm ^ 2).
Find the cross-sectional area of the new pipe S = S1 + S2 = 20.25P + 36P = 56.25P (cm ^ 2)
From the formula S = P * R ^ 2, we write down the radius of the new pipe. R ^ 2 = 56.26, then R = 7.5 cm.
Find the diameter d = 7.5 * 2 = 15 cm
Answer: 15 cm



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