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Calculating Areas of Circles and Sectors: A Comprehensive Guide

This guide explains how to calculate the area of a circle and sectors using mathematical formulas. It details the method to find the area based on given radius or diameter, including examples with both simple and complex calculations. Understand how to use the area formula (A = pi r^2) for circles and how to determine sector areas based on angles. Discover tips for accurate calculations and applications in real-world contexts, making geometry practical and engaging.

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Calculating Areas of Circles and Sectors: A Comprehensive Guide

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  1. a. Area = π (2.5)2 r= 2.5 cm ANSWER The area of A is about 19.63 square centimeters. Use the formula for area of a circle EXAMPLE 1 Find the indicated measure. SOLUTION A = πr2 Write formula for the area of a circle. Substitute 2.5 for r. = 6.25π Simplify. ≈ 19.63 Use a calculator.

  2. b. Diameter 113.1 = r2 π A = 113.1 cm2 ANSWER The radius is about 6 cm, so the diameter is about 12 centimeters. Use the formula for area of a circle EXAMPLE 1 Find the indicated measure. SOLUTION A = πr2 Write formula for the area of a circle. 113.1 = πr2 Substitute 113.1 for A. Divide each side by π. 6 ≈ r Find the positive square root of each side.

  3. Find the areas of the sectors formed by UTV. Because m UTV = 70°, mUV = 70° and mUSV = 360° – 70° = 290°. Find areas of sectors EXAMPLE 2 SOLUTION STEP 1 Find the measures of the minor and major arcs.

  4. mUV Area of small sector = πr2 360° 70° = π 82 360° Find areas of sectors EXAMPLE 2 STEP 2 Find the areas of the small and large sectors. Write formula for area of a sector. Substitute. ≈ 39.10 Use a calculator.

  5. 290° = π 82 360° ANSWER The areas of the small and large sectors are about 39.10 square units and 161.97 square units, respectively. mUSV Area of large sector = πr2 360° Find areas of sectors EXAMPLE 2 Write formula for area of a sector. Substitute. ≈ 161.97 Use a calculator.

  6. 1. Area of D ANSWER about 615.75 ft2 for Examples 1 and 2 GUIDED PRACTICE Use the diagram to find the indicated measure.

  7. ANSWER about 205.25 ft2 for Examples 1 and 2 GUIDED PRACTICE Use the diagram to find the indicated measure. 2. Area of red sector

  8. ANSWER about 410.50 ft2. for Examples 1 and 2 GUIDED PRACTICE Use the diagram to find the indicated measure. 3. Area of blue sector

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