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.

\color{red}64\pi square meters


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

Answer

\color{red}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

\color{red}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.

\color{red}60.00 square inches


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

Answer

\color{red}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

\color{red}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

\color{red}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

\color{red}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

\color{red}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

\color{red}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.

\color{red}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

\color{red}21\pi square inches


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