Germany · Klasse 6 · Practice Sheet 38

1. 1.

   Find the circumference of a circle whose radius is 16 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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2. 2.

   Find the perimeter of a rectangle measuring 31 m by 9 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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3. 3.

   Find the mean (average) of these numbers: 94, 11, 55, 89, 26.

   Formula:Arithmetic Mean

   $\bar{x} = \dfrac{\sum x}{n}$

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4. 4.

   An item costs €41.85 and you pay with €60. How much change do you get?

   Formula:Change Due

   $\text{change} = \text{paid} - \text{cost}$

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5. 5.

   €155 is shared in the ratio 2 : 3. Find each share.

   Formula:Dividing in a Ratio

   $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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6. 6.

   Find the area of a square with side length 13 cm.

   Formula:Area of a Square

   $A = s^2$

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7. 7.

   A triangle has a base of 20 cm and a height of 22 cm. Find its area.

   Formula:Area of a Triangle

   $A = \tfrac{1}{2} b h$

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8. 8.

   Find 7/8 of 104.

   Formula:Fraction of a Quantity

   $\text{result} = \dfrac{a}{b} \times N$

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9. 9.

   Find the circumference of a circle whose radius is 14 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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10. 10.

    €320 is shared in the ratio 5 : 3. Find each share.

    Formula:Dividing in a Ratio

    $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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11. 11.

    Find the mean (average) of these numbers: 78, 62, 79, 32, 53.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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12. 12.

    Find the area of a square with side length 15 cm.

    Formula:Area of a Square

    $A = s^2$

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13. 13.

    Calculate 144 ÷ 4.

    Formula:Division

    $q = \dfrac{a}{b}$

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14. 14.

    Find the perimeter of a rectangle measuring 17 m by 9 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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15. 15.

    A rectangle is 29 cm long and 12 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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16. 16.

    Find the area of a square with side length 12 cm.

    Formula:Area of a Square

    $A = s^2$

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17. 17.

    Calculate 115 ÷ 5.

    Formula:Division

    $q = \dfrac{a}{b}$

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18. 18.

    A car travels 385 km in 5 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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19. 19.

    A rectangle is 6 cm long and 15 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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20. 20.

    A train moves at 79 km/h for 2 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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