Italy · Classe 9 · Practice Sheet 24

1. 1.

   €84 is shared in the ratio 1 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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2. 2.

   A wave has frequency 399 Hz and wavelength 4.19 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A circle has a radius of 6 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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4. 4.

   A right-angled triangle has legs of 5 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   Find the gravitational potential energy of a 15 kg object raised 39 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Find the force needed to accelerate a 45 kg mass at 7.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   An object has mass 364.8 g and volume 48 cm³. Find its density.

   Formula:Density

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

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8. 8.

   €162 is shared in the ratio 3 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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9. 9.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    An object has mass 159 g and volume 30 cm³. Find its density.

    Formula:Density

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

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11. 11.

    Find the circumference of a circle whose radius is 18 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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12. 12.

    Find the gravitational potential energy of a 35 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A force of 15 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A cone has base radius 3 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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15. 15.

    A right-angled triangle has legs of 7 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    Find the gravitational potential energy of a 9 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A cylinder has radius 12 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    A device runs at 70 V drawing 7.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A cylinder has radius 8 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A current of 7.2 A flows through a 49 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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