Question

Introduction

Area is the space within a shape. The units of area are the squares of the units of length (that is, if a shape's sides are measured in meters, then the shape's area is measured in square meters).

For a circle, we will need to incorporate the constant pi, which we will approximate as the decimal 3.14.

To find the area of a circle, multiply pi (3.14) by the square of the radius. In other words, multiply pi times the radius times the radius.

For example, if a circle has a radius of 4m, the area is 3.14*4*4 = 50.24m2

If you are given a diameter instead of a radius, just remember that the radius is half of the diameter.

For example, if a circle has a diameter of 4m, then the radius is 2m, and the area is 3.14*2*2 = 12.56m2

Review

Directions: Calculate the area of a circle in each of the following problems.

1) d = 4.4 mm.

Calculate the area of the circle.

2) d = 3.7 cm.

Calculate the area of the circle.

3) r = 8.3 cm.

Calculate the area of the circle.

4) d = 5.8 yd.

Calculate the area of the circle.

5) d = 1 yd.

Calculate the area of the circle

6) r = 8 ft.

Calculate the area of the circle.

Answer 1

To calculate the area of a circle, we use the formula: Area = π * r^2, where π (pi) is approximately 3.14, and r is the radius of the circle.

Let's calculate the area of each circle based on the given values:

d = 4.4 mm.

Radius (r) = d / 2 = 4.4 mm / 2 = 2.2 mm

Area = π * (2.2 mm)^2 ≈ 15.21 mm²

d = 3.7 cm.

Radius (r) = d / 2 = 3.7 cm / 2 = 1.85 cm

Area = π * (1.85 cm)^2 ≈ 10.73 cm²

r = 8.3 cm.

Area = π * (8.3 cm)^2 ≈ 216.74 cm²

d = 5.8 yd.

Radius (r) = d / 2 = 5.8 yd / 2 = 2.9 yd

Area = π * (2.9 yd)^2 ≈ 26.39 yd²

d = 1 yd.

Radius (r) = d / 2 = 1 yd / 2 = 0.5 yd

Area = π * (0.5 yd)^2 ≈ 0.79 yd²

r = 8 ft.

Area = π * (8 ft)^2 ≈ 201.06 ft²

So, the areas of the circles are approximately:

15.21 mm²

10.73 cm²

216.74 cm²

26.39 yd²

0.79 yd²

201.06 ft²