Tanzania · Grade 9 · Practice Sheet 23

1. 1.

   A right-angled triangle has legs of 8 cm and 15 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A cylinder has radius 3 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   A device runs at 18 V drawing 1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the momentum of a 22 kg object moving at 4 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A current of 5.1 A flows through a 30 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A cylinder has radius 14 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   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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8. 8.

   A force of 53 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the momentum of a 58 kg object moving at 4 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A force of 295 N acts on an area of 5.9 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    TSh 500 is invested at 8% 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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12. 12.

    A device runs at 53 V drawing 4.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the force needed to accelerate a 50 kg mass at 0.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A value changes from 198 to 56. 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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15. 15.

    A right-angled triangle has legs of 16 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A cone has base radius 12 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    A value changes from 138 to 64. 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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18. 18.

    A bag has 26 equally likely marbles, of which 20 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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19. 19.

    Find the circumference of a circle whose radius is 23 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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20. 20.

    A circle has a radius of 12 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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