Area of a Circle Practice Problems with Answers

There are twelve (12) practice problems in this exercise about the area of the circle. You may use a calculator. Do not round intermediate calculations.

Round your final answer to two decimal places unless the exact answer is required.

For your convenience, I have included the different variations of formulas that you can use to find the area of a circle.

Three (3) formulas that you can use to find the area of a circle. The formulas are A=pi(r^2), A=((pi)d^2)/4, and A=C^2/(4pi)

Problem 1: What is the area of a circle with radius 8 meters? Leave your answer in terms of \large{\pi}.

Answer

This problem requires us to leave our answer in terms of \pi.

64\pi square meters


Problem 2: The diameter of a circle is 4.5 feet. Find its area. Use \pi = 3.1416.

Answer

15.90 square feet


Problem 3: Find the area of the circle below with a given radius. Use \pi = 3.14

a circle with radius 17 centimeters
Answer

907.46 square centimeters


Problem 4: Find the area of the circle below with a given diameter. Use the value of \pi on your calculator.

circle with radius 8.74 inches
Answer

Make sure that you use the internal value of \pi on your calculator.

60.00 square inches


Problem 5: The circumference of a circle is 22.2 feet. What is its area? Use \pi = 3.14

Answer

39.24 square feet


Problem 6: Determine the area of a dinner plate with a circumference of 37.68 inches. Use \pi = 3.14.

Answer

113.04 square inches


Problem 7: The radius of a circle is 5 inches. Find the area of the circle expressed in square centimeters c{m^2}. Use 1 in = 2.54 cm. Use \pi = 3.14.

Answer

Convert 5 inches to centimeters.

5 inches is equal to 12.7 centimeters

The area is

506.45 square centimeters


Problem 8: The diameter of a circle is 12.4 miles. Calculate the area of the circle in terms of square kilometers k{m^2}. Use 1 mi = 1.609 km. Use \pi = 3.1416.

Answer

Convert 12.4 miles to kilometers.

12.4 miles is equal to 19.9516 kilometers

The area is

312.64 square kilometers


Problem 9: What is the radius of a circle with an area of 73.12 square miles m{i^2}? Use \large{\pi = {{22} \over 7}}.

Answer

4.82 miles


Problem 10: Determine the diameter of the circle having an area of 100 square yards y{d^2}. Use \large{\pi = {{22} \over 7}}.

Answer

11.28 miles


Problem 11: Find the area of the semicircle below with a diameter of 8 centimeters. Use \pi = 3.1416.

semicircle with a diameter of 8 diameters
Answer

The area of a semicircle is half of the area of a circle.

27.33 square centimeters


Problem 12: Both circles share the same center. Find the exact area of the shaded region.

two circles that have the same center. the radius of the smaller circle is 2 inches while the larger circle is 5 inches.
Answer

Area of the shaded region = area of the larger circle minus area of the smaller (inner) circle

21\pi square inches


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