Długość Okręgu. Pole Koła

1. Liczba

jest liczbą niewymierną.

Prawda

Fałsz

The given statement is in Polish and it translates to "Number is an irrational number." The correct answer is "Prawda" which means "True" in English. This suggests that the statement is true and the number mentioned is indeed an irrational number.

Explanation

The given statement is in Polish and it translates to "Number is an irrational number." The correct answer is "Prawda" which means "True" in English. This suggests that the statement is true and the number mentioned is indeed an irrational number.

2. Koło o promieniu 10 i kwadrat mają taki sam obwód. Jaką długość ma bok kwadratu?

5

10

2,5

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. Since the circumference of the circle is equal to the perimeter of the square, we can set up the equation 2π(10) = 4x, where x is the length of one side of the square. Simplifying this equation, we get 20π = 4x. Dividing both sides by 4, we find that x = 5. Therefore, the length of one side of the square is 5.

Explanation

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. Since the circumference of the circle is equal to the perimeter of the square, we can set up the equation 2π(10) = 4x, where x is the length of one side of the square. Simplifying this equation, we get 20π = 4x. Dividing both sides by 4, we find that x = 5. Therefore, the length of one side of the square is 5.

3. Obwód koła jest

razy większy od jego średnicy.

Prawda

Fałsz

The statement is true because the circumference of a circle is always equal to pi times its diameter. Since the diameter is twice the length of the radius, the circumference is always approximately three times the length of the diameter. Therefore, the circumference is always greater than the diameter of a circle.

Explanation

The statement is true because the circumference of a circle is always equal to pi times its diameter. Since the diameter is twice the length of the radius, the circumference is always approximately three times the length of the diameter. Therefore, the circumference is always greater than the diameter of a circle.

4.

Jedną

Dwie

Trzy

Więcej niż trzy

not-available-via-ai

Explanation

not-available-via-ai

5. Jaką długość ma okrąg o średnicy 2?

2 * 3,14

2

4

4 * 3,14

The question asks for the length of a circle with a diameter of 2. The formula to calculate the circumference of a circle is 2 * π * r, where r is the radius. In this case, the diameter is given, so we can divide it by 2 to get the radius. Therefore, the radius is 1. Plugging this value into the formula, we get 2 * 3.14 = 6.28. However, none of the options provided match this value. The only option that matches the correct answer is 2, which is incorrect based on the given information. Therefore, the correct answer is not available.

Explanation

The question asks for the length of a circle with a diameter of 2. The formula to calculate the circumference of a circle is 2 * π * r, where r is the radius. In this case, the diameter is given, so we can divide it by 2 to get the radius. Therefore, the radius is 1. Plugging this value into the formula, we get 2 * 3.14 = 6.28. However, none of the options provided match this value. The only option that matches the correct answer is 2, which is incorrect based on the given information. Therefore, the correct answer is not available.

6. Ile karnawałowych opasek o średnicy 10 cm można wykonać z jednego metra wstążki?

Based on the given information, we know that one meter of ribbon is available. Since the diameter of each carnival headband is 10 cm, we can calculate the circumference of each headband using the formula C = πd, where d is the diameter. In this case, the circumference would be approximately 31.4 cm. Therefore, we can divide the length of the ribbon (100 cm) by the circumference of each headband (31.4 cm) to find out how many headbands can be made. The result is approximately 3 headbands. Hence, the correct answer is 3 opaski, 3opaski, 3.

Explanation

Based on the given information, we know that one meter of ribbon is available. Since the diameter of each carnival headband is 10 cm, we can calculate the circumference of each headband using the formula C = πd, where d is the diameter. In this case, the circumference would be approximately 31.4 cm. Therefore, we can divide the length of the ribbon (100 cm) by the circumference of each headband (31.4 cm) to find out how many headbands can be made. The result is approximately 3 headbands. Hence, the correct answer is 3 opaski, 3opaski, 3.

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7. Jaki promień ma koło, które na drodze 100 m obróciło się 25 razy?

Około 20 cm

Około 1,3 m

Około 80 cm

Około 0,6 m

The circumference of a circle is calculated by multiplying the radius by 2π. In this case, the circle has rotated 25 times along a distance of 100m. To find the radius, we can divide the distance traveled by the number of rotations. 100m divided by 25 rotations gives us 4m. However, this is the circumference of the circle. To find the radius, we need to divide the circumference by 2π. 4m divided by 2π is approximately 0.6366m, which is approximately equal to 0.6m. Therefore, the correct answer is approximately 0.6m.

Explanation

The circumference of a circle is calculated by multiplying the radius by 2π. In this case, the circle has rotated 25 times along a distance of 100m. To find the radius, we can divide the distance traveled by the number of rotations. 100m divided by 25 rotations gives us 4m. However, this is the circumference of the circle. To find the radius, we need to divide the circumference by 2π. 4m divided by 2π is approximately 0.6366m, which is approximately equal to 0.6m. Therefore, the correct answer is approximately 0.6m.

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9. Koło roweru o promieniu 0,4 m wykonało podczas jazdy 1000 obrotów. Jaką drogę pokonał rower w tym czasie?

The circumference of the bike wheel can be calculated using the formula C = 2πr, where r is the radius of the wheel. In this case, the radius is given as 0.4 m. Therefore, the circumference is C = 2π(0.4) = 0.8π m. Since the bike made 1000 rotations, the total distance traveled is 1000 times the circumference, which is 1000 * 0.8π = 800π m.

Explanation

The circumference of the bike wheel can be calculated using the formula C = 2πr, where r is the radius of the wheel. In this case, the radius is given as 0.4 m. Therefore, the circumference is C = 2π(0.4) = 0.8π m. Since the bike made 1000 rotations, the total distance traveled is 1000 times the circumference, which is 1000 * 0.8π = 800π m.

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