Questions: (i) A=πd^2 / 4 d=?

(i) A=πd^2 / 4 d=?
Transcript text: (i) $A=\pi d^{2} / 4$ $d=$ ?
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Solution

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Solution Steps

To solve for \( d \) in the equation \( A = \frac{\pi d^2}{4} \), we need to isolate \( d \). First, multiply both sides by 4 to eliminate the fraction, then divide by \(\pi\) to isolate \( d^2 \). Finally, take the square root of both sides to solve for \( d \).

Step 1: Rearrange the Equation

Start with the equation for the area of a circle in terms of diameter: \[ A = \frac{\pi d^2}{4} \]

Step 2: Eliminate the Fraction

Multiply both sides by 4 to eliminate the fraction: \[ 4A = \pi d^2 \]

Step 3: Isolate \( d^2 \)

Divide both sides by \(\pi\) to solve for \( d^2 \): \[ d^2 = \frac{4A}{\pi} \]

Step 4: Solve for \( d \)

Take the square root of both sides to solve for \( d \): \[ d = \sqrt{\frac{4A}{\pi}} \]

Step 5: Substitute the Given Value

Substitute \( A = 10 \) into the equation: \[ d = \sqrt{\frac{4 \times 10}{\pi}} \]

Step 6: Calculate the Value

Calculate the value of \( d \): \[ d \approx 3.568 \]

Final Answer

\[ \boxed{d = \sqrt{\frac{4A}{\pi}}} \]

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