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Nikitich [7]
4 years ago
7

Please help me with this

Mathematics
1 answer:
mafiozo [28]4 years ago
6 0

Answer:

<h2>a. 10cm</h2><h2>b. 5 cm</h2><h2>c. 31.4 cm</h2><h2>d. 78.5 cm²</h2><h2>e. 100 cm²</h2>

Step-by-step explanation:

Let:

<em>s - </em><em>side of the square</em>

<em>d - </em><em>diameter of the circle</em>

<em>r - </em><em>radius of a circle</em>

<em>C - </em><em>circumeference of the circle</em>

<em>AC - </em><em>area of the circle</em>

<em>AS - </em><em>area of a square</em>

The formula of a perimeter of a square:

<em>P = 4s</em>

We have <em>P = 40cm.</em>

Substitute:

<em>4s = 40              </em><em>divide both sides by 4</em>

<em>s = 10 cm</em>

a.

The length of the diameter of the circle inscribed in the square is equal to the length of the side of the square.

Therefore <em>d = s → d = 10 cm.</em>

b.

The length of the circle diameter is two lengths of the circle radius.

Therefore <em>d = 2r → r = d : 2 → r = 10 : 2 = 5 cm.</em>

c.

The formula of a circumference of a circle:

<em>C = dπ.</em>

Substitute <em>d = 10cm</em>, and <em>π = 3.14.</em>

<em>C = 10(3.14) = 31.4 cm.</em>

d.

The formula of an area of a circle:

<em>AC = πr²</em>

Substitute <em>r = 5cm</em> and <em>π = 3.14</em>

<em>AC = 3.14(5²) = 3.14(25) = 78.5 cm²</em>.

e.

The formula of an area of a square:

<em>AS = s²</em>

Substitute <em>s = 10 cm</em>

<em>AS = 10² = 100 cm²</em>

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