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 $\pi = 3.14$

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.

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.

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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