The area of a circle, denoted by A, is calculated using the formula A = π r², where r represents the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14159.

We are given that the area of the circle is 32 cm². We substitute this value into the area formula, setting A = 32.

Area of circle is 32 cm² what were the radius of the circle be?

Answer: The radius of the circle is $\sqrt{\frac{32}{\pi}} \text{ cm}$ or approximately $3.19 \text{ cm}$ .

Step-by-step solution

Step 1: Recall the formula for the area of a circle

The area of a circle, denoted by $A$ , is calculated using the formula $A = \pi r^2$ , where $r$ represents the radius of the circle and $\pi$ (pi) is a mathematical constant approximately equal to $3.14159$ .

Step 2: Substitute the given area into the formula

We are given that the area of the circle is $32 \text{ cm}^2$ . We substitute this value into the area formula, setting $A = 32$ .

Step 3: Isolate the radius squared term

To find the radius, we need to isolate $r$ . First, we divide both sides of the equation by $\pi$ to get an expression for $r^2$ .

Step 4: Solve for the radius

To find $r$ , we take the square root of both sides of the equation. Since the radius must be a positive value, we only consider the positive square root.

Step 5: Calculate the approximate value of the radius

Using the approximate value of $\pi \approx 3.14159$ , we can calculate the numerical value of the radius. The radius is approximately $3.19 \text{ cm}$ .

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