Carpentry & Building Construction © 2004

Math Activities :

Self-Check Math Activity 24

Area of a Circle

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Carpenters need to be able to calculate the area of a circle. The area of a circle can be found by multiplying pi times the radius squared (the radius multiplied by itself). The formula for the area of a circle is A = πr2, where A is the area of the circle, π is a constant, and r is the radius of the circle. The value of π is approximately 3.1416.

Terms, Symbols, & Abbreviations
area - the amount of space within a flat figure
pi, or π - the ratio of the circumference of a circle to its diameter, approximately 3.1416
diameter - the length of a straight line through the center of a circle
radius - one-half the distance of the diameter
sq. in. = square inch, or square inches
sq. ft. = square foot, or square feet. One sq. ft. = 144 sq. in.
sq. yd. = square yard, or square yards. One sq. yd. = 9 sq. ft.

Practice Exercise

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Find the area of the circle. Round your answer to the nearest hundredth.
Step 1 The formula is A = πr2
Step 2 Insert the known values.
  A = 3.1416 × 72
Step 3 A = 3.1416 × 49
Step 4 A = 153.9384
Step 5 Round off to nearest hundredth.
  A = 153.94 sq. in.
Find the area of a circle whose diameter is 8''.
Step 1 Diameter = 2 times the radius, so 8/2 = 4.
Step 2 Insert the known values into the formula A = πr2.
  A = 3.1416 × 42
Step 3 A = 3.1416 × 16
Step 4 A = 50.2656
Step 5 Round off to nearest hundredth.
  A = 50.27 sq. in.

Problem Exercises

Round your answers to the nearest hundredth.

1.
Find the area of a circle whose diameter is 3'.
A)3.53 sq. ft.
B)7.07 sq. ft.
C)14.14 sq. ft.
D)28.27 sq. ft.
2.
Find the area of a circle whose radius is 7.5'.
A)22.09 sq. ft.
B)44.18 sq. ft.
C)88.36 sq. ft.
D)176.71 sq. ft.
3.
A contractor is preparing specs for a 12' diameter raised platform. The area of the platform floor is
A)28.27 sq. ft.
B)56.55 sq. ft.
C)113.10 sq. ft.
D)452.39 sq. ft
4.
A carpenter will cut an opening for a custom window with a 1.5' radius and an area of
A)7.07 sq. ft.
B)14.14 sq. ft.
C)28.27 sq. ft.
D)56.55 sq. ft.
5.
A 10' diameter hole for an excavation is marked by a circle whose area is
A)39.27 sq. ft.
B)78.54 sq. ft.
C)157.08 sq. ft.
D)314.16 sq. ft.
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