Russia · Grade 9 · Practice Sheet 46

1. 1.

   A cylinder has radius 8 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.

   Find the circumference of a circle whose radius is 12 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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3. 3.

   An object has mass 176.3 g and volume 41 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A car travels 148 km in 2 hours. Find its average speed.

   Formula:Speed

   $v = \dfrac{d}{t}$

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5. 5.

   Find the momentum of a 44 kg object moving at 23 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the circumference of a circle whose radius is 11 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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7. 7.

   A right-angled triangle has legs of 13 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   ₽2,800 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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9. 9.

   A cone has base radius 11 cm and height 13 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.

    ₽190 is shared in the ratio 5 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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11. 11.

    A current of 0.9 A flows through a 50 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A right-angled triangle has legs of 4 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.

    A value changes from 41 to 148. 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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14. 14.

    ₽3,300 is invested at 5% compound interest per annum for 2 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 train moves at 44 km/h for 3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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16. 16.

    A 6 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    A car travels 188 km in 4 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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18. 18.

    A device runs at 130 V drawing 3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A value changes from 148 to 34. 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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20. 20.

    A current of 6.7 A flows through a 27 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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