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An engineer is planning a new water pipe installation. The circular pipe has a diameter of 
d=20cm.
What is the area 
A of the circular cross section of this pipe?
Give your answer in terms of pi.

An engineer is planning a new water pipe installation. The circular pipe has a diameter of d=20 cm d=20 \mathrm{~cm} .\newlineWhat is the area A A of the circular cross section of this pipe?\newlineGive your answer in terms of pi.\newlineA=A=\square cm2cm^{2}

Full solution

Q. An engineer is planning a new water pipe installation. The circular pipe has a diameter of d=20 cm d=20 \mathrm{~cm} .\newlineWhat is the area A A of the circular cross section of this pipe?\newlineGive your answer in terms of pi.\newlineA=A=\square cm2cm^{2}
  1. Circle Area Formula: The formula for the area of a circle is A=πr2A = \pi r^2, where rr is the radius.
  2. Find Radius: First, find the radius of the circle. The radius is half of the diameter, so r=d2r = \frac{d}{2}.
  3. Calculate Radius: The diameter dd is given as 20cm20\,\text{cm}, so the radius rr is 20cm20\,\text{cm} / 22 = 10cm10\,\text{cm}.
  4. Plug into Formula: Now, plug the radius into the area formula: A=π(10cm)2A = \pi(10\,\text{cm})^2.
  5. Calculate Area: Calculate the area: A=π(100cm2)A = \pi(100\,\text{cm}^2).
  6. Final Result: The area of the circular cross section is A=100πcm2A = 100\pi \, \text{cm}^2.

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