South Africa · Grade 10 · Practice Sheet 30

1. 1.

   A cylinder has radius 10 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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2. 2.

   A cone has base radius 2 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   A right-angled triangle has legs of 13 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 9 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   Find the momentum of a 7 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A wave has frequency 651 Hz and wavelength 4.83 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   R3,300 is invested at 6% compound interest per annum for 4 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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8. 8.

   A value changes from 61 to 220. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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9. 9.

   Find the gravitational potential energy of a 15 kg object raised 34 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    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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11. 11.

    A wave has frequency 118 Hz and wavelength 2.59 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A cone has base radius 4 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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13. 13.

    A device runs at 125 V drawing 5.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A force of 75 N acts on an area of 4.2 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A 7 kg object moves at 20 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    Find the momentum of a 50 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A wave has frequency 621 Hz and wavelength 0.55 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A device runs at 145 V drawing 0.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the force needed to accelerate a 30 kg mass at 2.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A current of 2.3 A flows through a 28 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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