An engineer is planning a new water pipe installation. The circular pipe has a diameter of \( d = 20 \text{ cm} \). What is the area \( A \) of the circular cross-section of this pipe? Provide your answer in terms of \(\pi\).
Mathematics · Middle School · Thu Feb 04 2021
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Answer: To calculate the area \( A \) of the circular cross-section of the pipe, we will use the formula for the area of a circle:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle. Since the diameter \( d \) of the pipe is given as 20 cm, we can find the radius by dividing the diameter by 2:
\[ r = \frac{d}{2} = \frac{20 \text{ cm}}{2} = 10 \text{ cm} \]
Now we can substitute the radius into the area formula:
\[ A = \pi (10 \text{ cm})^2 \] \[ A = \pi \times 100 \text{ cm}^2 \] \[ A = 100\pi \text{ cm}^2 \]
Thus, the area \( A \) of the circular cross-section of the pipe is \( 100\pi \text{ cm}^2 \).