Egypt · Grade 10 · Practice Sheet 16

1. 1.

   A cone has base radius 12 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   A wave has frequency 250 Hz and wavelength 3.49 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Solve using the quadratic formula: x² + 0x − 9 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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4. 4.

   A force of 120 N acts on an area of 8.4 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A wave has frequency 825 Hz and wavelength 1.82 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the gravitational potential energy of a 23 kg object raised 37 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A cylinder has radius 7 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   A triangle has sides a = 18 cm and b = 15 cm with an included angle C = 120°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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9. 9.

   Find the momentum of a 48 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A device runs at 146 V drawing 6.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the momentum of a 24 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Solve using the quadratic formula: x² + 4x + 3 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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13. 13.

    A right-angled triangle has legs of 10 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    A current of 1.7 A flows through a 56 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 3 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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16. 16.

    A force of 120 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A wave has frequency 571 Hz and wavelength 3.95 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A cone has base radius 7 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    A current of 5.6 A flows through a 47 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    Find the force needed to accelerate a 40 kg mass at 6.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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