Germany · Klasse 9 · Practice Sheet 14

1. 1.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   €156 is shared in the ratio 5 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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3. 3.

   Find the gravitational potential energy of a 27 kg object raised 11 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A wave has frequency 53 Hz and wavelength 0.42 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   An object has mass 171.1 g and volume 29 cm³. Find its density.

   Formula:Density

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

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6. 6.

   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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7. 7.

   Solve for x: 6x + 7 = 31.

   Formula:Solving a Linear Equation

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

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8. 8.

   A right-angled triangle has legs of 15 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   A 29 kg object moves at 25 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    Find the momentum of a 2 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

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

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A right-angled triangle has legs of 15 cm and 14 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    €3,200 is invested at 6% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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15. 15.

    A wave has frequency 765 Hz and wavelength 1.93 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Find the force needed to accelerate a 26 kg mass at 2.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A 38 kg object moves at 22 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    A device runs at 6 V drawing 2.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    An object has mass 30 g and volume 6 cm³. Find its density.

    Formula:Density

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

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20. 20.

    A train moves at 40 km/h for 4.6 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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