Grade 8, Vol 2 Math Student Handbook

WORKING WITH CIRCLES

As a wind turbine’s blades rotate, they cover a circular area called the blade sweep. The maximum power that a wind turbine can generate is proportional to the area of the blade sweep. You can use the parts of a circle to determine the blade sweep and other properties of the turbines.

radius = 115 ft

EXAMPLE: A prototype wind turbine has a diameter of 230 feet. What’s its blade sweep?

diameter = 2 × radius = 230 ft

Find the radius of the circle. Since the diameter is given, you divide by 2.

circumference = 2 × radius = 722.2 ft

230 feet 2

= 115 feet

Square the radius.

115 feet × 115 feet = 13,225 ft 2

Multiply by pi. Use the approximation 3.14.

13,225 × 3.14 = 41,526.5 ft 2

Round your answer to the nearest hundred.

area = (radius) 2 = (115) 2

41,526.5 ft 2 ≈ 41,500 ft 2

= 41,526.5 ft 2

So the blade sweep is about 41,500 ft 2 .

Use the properties of circles to answer the questions about wind turbines that follow. Round all blade sweeps to the nearest hundred and circumferences and radii to the nearest whole number.

1 Complete the missing

2 Highlight the wind farm whose turbines have the greatest blade sweep, for a single turbine, in yellow.

3 Highlight the wind farm that has the greatest combined blade sweep, based on the total number of turbines, in green.

entries in the chart of wind

turbines below.

NUMBER OF TURBINES

TURBINE RADIUS

TURBINE CIRCUMFERENCE

TURBINE BLADE SWEEP

OFFSHORE WIND FARM LOCATION

Block Island Wind Farm

5

1,500 ft

U.S.

Burbo Bank Extension

32

269 ft

U.K.

140

96,700 ft 2

U.K.

Greater Gabbard

48

960 ft

Sweden

Lillgrund

34

68,300 ft2

China

Donghai Bridge

80 200 ft

Germany

Bard Offshore 1

SOURCE: Websites of companies

30/07/21 10:38 AM

Sessions 27 & 28 79

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