Questions: (i) A=πd^2 / 4 d=?

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

Solution

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 $: \[ d \approx 3.568 \]