Ecuador · Grado 9 · Practice Sheet 17

1. 1.

   A right-angled triangle has legs of 17 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   An object has mass 63.2 g and volume 8 cm³. Find its density.

   Formula:Density

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

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3. 3.

   A car travels 186 km in 3 hours. Find its average speed.

   Formula:Speed

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

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4. 4.

   A device runs at 198 V drawing 2.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the force needed to accelerate a 38 kg mass at 8.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   Find the gravitational potential energy of a 26 kg object raised 36 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A train moves at 48 km/h for 3.3 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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9. 9.

   A cylinder has radius 5 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A car travels 180 km in 5 hours. Find its average speed.

    Formula:Speed

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

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11. 11.

    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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12. 12.

    A bag has 26 equally likely marbles, of which 23 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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13. 13.

    $216 is shared in the ratio 4 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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14. 14.

    Find the gravitational potential energy of a 49 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Find the force needed to accelerate a 54 kg mass at 7.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A 30 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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17. 17.

    A circle has a radius of 17 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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18. 18.

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

    Formula:Dividing in a Ratio

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

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19. 19.

    An object has mass 44.8 g and volume 32 cm³. Find its density.

    Formula:Density

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

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20. 20.

    Find the force needed to accelerate a 54 kg mass at 8.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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