The area of a circle is the space enclosed within its boundary. It is calculated using the formula A = π r², where A is the area, π (pi) is a mathematical constant approximately equal to 3.14159 or (22)/(7), and r is the radius of the circle.

The area of a circle is the space enclosed within its boundary. It is calculated using the formula A = π r², where A is the area, π (pi) is a mathematical constant approximately equal to 3.14159 or (22)/(7), and r is the radius of the circle.

We are given that the radius r = 7 cm. We will use the common approximation for π, which is (22)/(7). Substitute these values into the area formula.

First, calculate the square of the radius: 7² = 49. Then, multiply this by (22)/(7). The 7 in the denominator will cancel out with one of the 7 s from 49 (since 49 = 7 × 7), leaving 22 × 7.

Perform the final multiplication: 22 × 7 = 154. The area is expressed in square centimeters.

Find the area of a circle with radius 7 cm

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Step-by-Step Solution

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

The area of a circle is the space enclosed within its boundary. It is calculated using the formula $A = \pi r^2$ , where $A$ is the area, $\pi$ (pi) is a mathematical constant approximately equal to $3.14159$ or $\frac{22}{7}$ , and $r$ is the radius of the circle.

Step 2: Substitute the given values

We are given that the radius $r = 7 \text{ cm}$ . We will use the common approximation for $\pi$ , which is $\frac{22}{7}$ . Substitute these values into the area formula.

Step 3: Calculate the area

First, calculate the square of the radius: $7^2 = 49$ . Then, multiply this by $\frac{22}{7}$ . The $7$ in the denominator will cancel out with one of the $7$ s from $49$ (since $49 = 7 \times 7$ ), leaving $22 \times 7$ .

Step 4: Final calculation

Perform the final multiplication: $22 \times 7 = 154$ . The area is expressed in square centimeters.