Hungary · Grade 9 · Practice Sheet 4

1. 1.

   A cone has base radius 9 cm and height 17 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.

   Find the gravitational potential energy of a 50 kg object raised 10 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Ft 1,800 is invested at 5% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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4. 4.

   A force of 52 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A bag has 20 equally likely marbles, of which 3 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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6. 6.

   A force of 18 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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7. 7.

   A right-angled triangle has legs of 19 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   A force of 329 N acts on an area of 9.4 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A cone has base radius 12 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A cylinder has radius 6 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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11. 11.

    An object has mass 231.4 g and volume 26 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A force of 301 N acts on an area of 9.1 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A bag has 22 equally likely marbles, of which 5 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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14. 14.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    A current of 1.8 A flows through a 49 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Solve for x: 8x + 4 = 44.

    Formula:Solving a Linear Equation

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

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17. 17.

    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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18. 18.

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

    Formula:Pythagorean Theorem

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

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19. 19.

    A wave has frequency 308 Hz and wavelength 1.54 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A right-angled triangle has legs of 3 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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