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Problem of the Day

A 16 in. pizza sells for $11.99. A 10 in. pizza sells for $5.99. Which size gives you more pizza per penny? Explain.

The larger pizza; you get more than twice as much (64 in2 instead of 25in2) for about twice the price.

Sunshine State Standards

Prep for MA.7.G.2.1 Justify and use formulas for surface area and volume of pyramids, prisms, cylinders, and cones.

Review of MA.6.G.4.1

A circle can be cut into equal-sized sectors and arranged to resemble a parallelogram. The height h of the parallelogram is equal to the radius r of the circle, and the base b of the parallelogram is equal to one-half the circumference C of the circle.

So the area of the parallelogram can be written as

1

2

Cr.

A = bh, or A =

1

2

Since C = 2r, A =

(2r)r = r2.

Remember!

The order of operations calls for evaluating the exponents before multiplying.

Additional Example 1A: Finding the Area of a Circle

Find the area of the circle to the nearest tenth. Use 3.14 for .

A = r2

Use the formula.

7 cm

A 3.14 · 72

Substitute 7 for r.

A 3.14 · 49

Evaluate the power.

Multiply.

A 153.86

The area of the circle is about 153.9 cm2.

Additional Example 1B: Finding the Area of a Circle

Find the area of the circle to the nearest tenth. Use 3.14 for .

A = r2

Use the formula.

A 3.14 · 92

Substitute 9 for r.

18 ft

A 3.14 · 81

Evaluate the power.

Multiply.

A 254.34

The area of the circle is about 254.3 ft2.

Check It Out: Example 1A

Find the area of the circle to the nearest tenth. Use 3.14 for .

A = r2

Use the formula.

A 3.14 · 102

10 cm

Substitute 10 for r.

A 3.14 · 100

Evaluate the power.

Multiply.

A 314

The area of the circle is about 314 cm2.

Check It Out: Example 1B

Find the area of the circle to the nearest tenth. Use 3.14 for .

A = r2

Use the formula.

12 ft

A 3.14 · 62

Substitute 6 for r.

A 3.14 · 36

Evaluate the power.

Multiply.

A 113.04

The area of the circle is about 113.0 ft2.

Additional Example 2: Application

Park employees are fitting a top over a circular drain in the park. If the radius of the drain is 14 inches, what is the area of the top that will cover the drain? Use

22

7

for .

A = r2

Use the formula for the area of a circle.

22

7

·142

Substitute. Use 14 for r.

A

28

22

7

196

·

A

Evaluate the power.

1

A 22 · 28

Multiply.

A 616

The area of the top that will cover the drain is about 616 in2.

Check It Out: Example 2

Albert was designing a cover for a spa. If the radius of the spa is 7 ft, what is the area of the cover that will be made? Use

22

7

for .

A = r2

Use the formula for the area of a circle.

22

7

·72

A

Substitute. Use 7 for r.

7

22

7

49

·

A

Evaluate the power.

1

A 22 · 7

Multiply.

A 154

The area of the top that will cover spa is about 154 ft2.

Additional Example 3: Application

Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth.

1.5 cm

The measurement of the radius of the circle is 1.5 cm.

Now find the area of the entire circle.

A = r2

Use the formula for the area of a circle.

Substitute. Use 1.5 for r.

A = 3.14 · 1.52

A 3.14 · 2.25

Evaluate the power.

Multiply.

A 7.07

1 2

Since of the circle is shaded, divide the area of the

circle by 2. 7.07 ÷ 2 = 3.535.

Additional Example 3 Continued

Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth.

The area of the shaded region of the circle is about 3.5 cm2.

Check It Out: Example 3

Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth.

2.4 cm

The measurement of the radius of the circle is 2.4 cm.

Now find the area of the entire circle.

A = r2

Use the formula for the area of a circle.

Substitute. Use 2.4 for r.

A = 3.14 · 2.42

A 3.14 · 5.76

Evaluate the power.

Multiply.

A 18.09

3 4Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth.

Since of the circle is shaded, divide the area of the

circle by 4 and subtract the answer from the entire area. 18.0864 ÷ 4 = 4.52. 18.0864 – 4.52 = 13.56.

Check It Out: Example 3 Continued

The area of the shaded region of the circle is about 13.56 cm2.

Lesson Quiz

Find the area of each circle, to the nearest tenth. Use 3.14 for .

1.

3. The bull’s-eye on a target has a diameter of 2 in.What is the area of the bull’s-eye to the nearest tenth? Use 3.14 for .

4. A round tablecloth has a radius of 36 in. What isthe area of the tablecloth? Use 3.14 for . Roundyour answer to the nearest tenth.

8 ft

2.

9 ft

•

201.0 ft2

•

63.6 ft2

3.1 in2

4,069.4 in2

Lesson Quiz for Student Response Systems

1. Identify the area of the circle to the nearest tenth. Use 3.14 for .

A. 907.5 ft2

B. 289 ft2

C. 226.9 ft2

D. 53.4 ft2

17 ft

Lesson Quiz for Student Response Systems

2. Identify the area of the circle to the nearest tenth. Use 3.14 for .

A. 72.2 in2

B. 144.4 in2

C. 415.3 in2

D. 1661.1 in2

23 in.

Lesson Quiz for Student Response Systems

3. A round table has a diameter of 11 ft. What is the area of the table to the nearest tenth? Use 3.14 for .

A. 95 ft2

B. 69.1 ft2

C. 54.2 ft2

D. 34 ft2

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