Practice on the area of a circle

### 1.1. Solve the exercises in the textbook Practice page 100

Lesson 1 Textbook page 100

Calculate the area of a circle with radius r:

a) r = 6cm b) r = 0.35dm

__Solution guide:__

a) The area of the circle is:

6 × 6 × 3.14 = 113.04(cm^{2})

b) The area of the circle is:

0.35 × 0.35 × 3.14 = 0.38465(dm^{2})

Lesson 2 Textbook page 100

Find the area of a circle with perimeter C=6.28cm.

__Solution guide:__

The radius of the circle is:

6.28 : 3.14 : 2 = 1(cm)

The area of the circle is:

1×1×3.14=3.14(cm^{2})

Answer: 3.14cm^{2}

Lesson 3 Textbook page 100

The mouth of the well is a circle with a radius of 0.7. People built a 0.3m wide well around the mouth of the well. Calculate the area of the well wall.

__Solution guide:__

The area of the small circle (well mouth) is:

0.7×0.7×3.14=1.5386(m2)

The radius of the crossed circle is:

0.7+0.3=1(m)

The area of the crossed circle (or the area of the large circle) is:

1×1×3.14=3.14(m2)

The area of the well wall is:

3.14−1.5386=1.6014(m2)

Answer: 1.6014m2

### 1.2. Solving exercises in textbooks General practice pages 100, 101

Lesson 1 Textbook page 100

A steel wire is bent as shown below. Calculate the length of the rope.

__Solution guide:__

The circumference of a circle with radius 7cm is:

7×2×3.14=43.96(cm)

The circumference of a circle with radius 10 cm is:

10×2×3.14=62.8(cm)

The length of the steel wire is:

43.96+62.8=106.76(cm)

Answer: 106.76cm

Lesson 2 Textbook page 100

The two circles have the same center O as the figure below. How many centimeters longer is the circumference of the larger circle than the circumference of the smaller circle?

__Solution guide:__

The radius of the great circle is:

60+15=75(cm)

The circumference of the great circle is:

75×2×3.14=471(cm)

The circumference of the small circle is:

60×2×3.14=376.8(cm)

The circumference of the larger circle is several centimeters longer than the circumference of the small circle:

471−376.8=94.2(cm)

Answer: 94.2cm

Lesson 3 Textbook page 101

The figure below is made up of a rectangle and two semicircles (see figure). Calculate the area of the figure.

__Solution guide:__

The area of the given figure is equal to the sum of the areas of the rectangle and the two semicircles.

The sum of the areas of two semicircles is equal to the area of the circle with radius square meter

$7c\mathrm{square\; meter}$.

The length of the rectangle is:

2=14(csquare meter)

The area of the rectangle is:

ten=140(csquare meter^{2})

The area of the two semicircles is:

7×3,14=153,eighty six(csquare meter^{2})

The area of the given figure is:

153,eighty six=293,eighty six(csquare meter^{2})

Answer: eighty sixcsquare meter^{2}

Lesson 4 Textbook page 101

Choose a letter that has a right answer:

The area of the shaded part of square ABCD is:

A 13.76cm^{2} B. 114.24cm^{2}

C. 50.24cm^{2} D. 136.96cm^{2}

__Solution guide:__

A circle with center O has a diameter equal to the length of the side of the square and 8 cm.

The radius of a circle with center O is:

8: 2 = 4 (cm)

The area of a circle with center O is:

4 x 4 x 3.14 = 50.24 (cm^{2})

The area of square ABCD is:

8 x 8 = 64 (cm^{2})

The area of the shaded part is:

64 – 50.24 = 13.76 (cm^{2})

Choose answer A

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