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Estimating and Calculating the Area of Circles in California Standards

Learn how to estimate and calculate the area of circles using common estimates of pi (3.14) and compare with actual measurements. Also covers concepts of sectors and parallelograms.

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Estimating and Calculating the Area of Circles in California Standards

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  1. California Standards MG1.2 Know common estimates of  (3.14; ) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements. Also covered:AF3.1, AF3.2, t MG1.1 227

  2. A circle can be cut into equal-sized sectors and arranged to resemble a parallelogram. The height h of the parallelogram is equal to the radius r of the circle, and the base b of the parallelogram is equal to one-half the circumference C of the circle. So the area of the parallelogram can be written as 1 2 Cr. A = bh, or A = 1 2 Since C = 2r, A = (2r)r = r2.

  3. Additional Example 1: Estimation Application Find the area of the circle by using a formula. Then use an estimate to check whether your answer is reasonable. A = r2 Use the formula. Use 3.14 as an estimate for p, and use 3 for r. A 3.14· 32 A  3.14 · 9 Evaluate the power. Multiply. A 28.26 square units

  4. Additional Example 1 Continued Find the area of the circle by using a formula. then use an estimate to check whether your answer is reasonable. Check Use the grid to estimate the area. 16 squares are completely inside the circle. 8 squares are mostly inside the circle. 8 squares are halfway inside the circle. 16 + 8 + ½(8) = 28 square units Because 28 is close to 28.26, an answer of 28.26 square units is reasonable.

  5. Check It Out! Example 1 Find the area of the circle by using a formula. then use an estimate to check whether your answer is reasonable. A = r2 Use the formula. Use 3.14 as an estimate for p, and use 2 for r. A 3.14· 22 A  3.14 · 4 Evaluate the power. Multiply. A 12.56

  6. Check It Out! Example 1 Continued Find the area of the circle by using a formula. then use an estimate to check whether your answer is reasonable. Check Use the grid to estimate the area. 4 squares are completely inside the circle. 8 squares are mostly inside the circle. 4 + 8 + = 12 square units Because 12 is close to 12.56, an answer of 12.56 square units is reasonable.

  7. Additional Example 2: Finding the Area of a Circle A. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for . A = r2 Use the formula. 7 cm A 3.14 · 72 Substitute 7 for r. A 3.14 · 49 Evaluate the power. Multiply. A  153.86 The area of the circle is about 153.9 cm2.

  8. Additional Example 2: Finding the Area of a Circle B. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for . A = r2 Use the formula. A 3.14 · 92 Substitute 9 for r. 18 ft A 3.14 · 81 Evaluate the power. Multiply. A  254.34 The area of the circle is about 254.3 ft2.

  9. Check It Out! Example 2 A. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for . A = r2 Use the formula. A 3.14 · 102 10 cm Substitute 10 for r. A 3.14 · 100 Evaluate the power. Multiply. A  314 The area of the circle is about 314 cm2.

  10. Check It Out! Example 2 B. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for . A = r2 Use the formula. 12 ft A 3.14 · 62 Substitute 6 for r. A 3.14 · 36 Evaluate the power. Multiply. A  113.04 The area of the circle is about 113.0 ft2.

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