Colombia · Grado 8 · Practice Sheet 6

1. 1.

   A right-angled triangle has legs of 3 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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2. 2.

   A force of 313 N acts on an area of 7.3 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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3. 3.

   A cylinder has radius 10 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   A triangle has a base of 21 cm and a height of 12 cm. Find its area.

   Formula:Area of a Triangle

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

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5. 5.

   A cylinder has radius 12 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   An object has mass 119 g and volume 17 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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7. 7.

   A current of 2.7 A flows through a 37 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   An object has mass 230.4 g and volume 32 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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9. 9.

   Find the mean (average) of these numbers: 88, 11, 31, 73.

   Formula:Arithmetic Mean

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

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10. 10.

    An object has mass 52.8 g and volume 22 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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11. 11.

    A value changes from 95 to 82. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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12. 12.

    A circle has a radius of 25 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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13. 13.

    A cylinder has radius 12 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    A triangle has a base of 11 cm and a height of 7 cm. Find its area.

    Formula:Area of a Triangle

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

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15. 15.

    Solve for x: 9x + 15 = 87.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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16. 16.

    Find the circumference of a circle whose radius is 15 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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17. 17.

    A train moves at 39 km/h for 4.6 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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18. 18.

    A bag has 30 equally likely marbles, of which 11 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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19. 19.

    $110 is shared in the ratio 3 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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20. 20.

    A right-angled triangle has legs of 13 cm and 14 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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