We are given the radius of the circle, r, as 6 cm, and the angle of the sector, θ, as 60 degrees. We also need to use the approximation π ≈ 3.14.

Now we substitute the given values of θ = 60^(°), π = 3.14, and r = 6 cm into the formula for the area of a sector. This sets up the calculation.

First, we simplify the fraction (60^(°))/(360^(°)), which reduces to (1)/(6). This makes the subsequent calculations easier.

Next, we calculate the square of the radius, 6², which is 36 cm².

Now, we multiply (1)/(6) by 36 cm², which simplifies to 6 cm². The expression becomes 6 multiplied by 3.14.

Finally, we perform the last multiplication: 6 × 3.14 = 18.84. This gives us the area of the sector in square centimeters.

Find the area of a sector of a circle with radius 6 cm if the angle of the sector is 60 degrees. (Use $\pi \approx 3.14$ )

Answer: The area of the sector is $18.84 \text{ cm}^2$ .

Step-by-step solution

Step 1: Identify Given Values

We are given the radius of the circle, $r$ , as $6 \text{ cm}$ , and the angle of the sector, $\theta$ , as $60$ degrees. We also need to use the approximation $\pi \approx 3.14$ .

Step 2: Formula for Area of a Sector

To find the area of a sector, we use the formula that relates the central angle of the sector to the total angle of a circle ( $360^{\circ}$ ).

Step 3: Substitute Values into Formula

Now we substitute the given values of $\theta = 60^{\circ}$ , $\pi = 3.14$ , and $r = 6 \text{ cm}$ into the formula for the area of a sector. This sets up the calculation.

Step 4: Simplify the Fraction

First, we simplify the fraction $\frac{60^{\circ}}{360^{\circ}}$ , which reduces to $\frac{1}{6}$ . This makes the subsequent calculations easier.

Step 5: Calculate the Square of the Radius

Next, we calculate the square of the radius, $6^2$ , which is $36 \text{ cm}^2$ .

Step 6: Perform Multiplication

Now, we multiply $\frac{1}{6}$ by $36 \text{ cm}^2$ , which simplifies to $6 \text{ cm}^2$ . The expression becomes $6$ multiplied by $3.14$ .

Step 7: Final Calculation

Finally, we perform the last multiplication: $6 \times 3.14 = 18.84$ . This gives us the area of the sector in square centimeters.

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Find the area of a sector of a circle with radius 6 cm if the angle of the sector is 60 degrees. (Use π≈3.14\pi \approx 3.14π≈3.14)