If the radius r = 7 cm, what is the circle's area? Provide both exact form and decimal approximation.

If the radius r = 7 cm, what is the circle's area? Provide both exact form and decimal approximation.

• A. 14π cm^2 and 87.96 cm^2
• B. 98 cm^2 and 31.62 cm^2
• C. 49π cm^2 and 153.94 cm^2
• D. 7π cm^2 and 21.99 cm^2

Answer: (C)

Area of a circle is found using A = π r^2. With radius 7 cm, r^2 = 49, so A = π × 49 = 49π cm^2. The decimal approximation uses π ≈ 3.14159265, giving 49 × 3.14159265 ≈ 153.94 cm^2 (rounded to two decimals). So the exact form is 49π cm^2 and the decimal form is 153.94 cm^2. Other options would imply a different radius or produce a decimal that doesn’t match 49π, so they don’t align with r = 7.

Area of a circle is found using A = π r^2. With radius 7 cm, r^2 = 49, so A = π × 49 = 49π cm^2. The decimal approximation uses π ≈ 3.14159265, giving 49 × 3.14159265 ≈ 153.94 cm^2 (rounded to two decimals). So the exact form is 49π cm^2 and the decimal form is 153.94 cm^2. Other options would imply a different radius or produce a decimal that doesn’t match 49π, so they don’t align with r = 7.