Russia · Grade 9 · Practice Sheet 16

1. 1.

   Find the circumference of a circle whose radius is 22 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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2. 2.

   A train moves at 36 km/h for 5.5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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3. 3.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   A wave has frequency 112 Hz and wavelength 3.82 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   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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6. 6.

   An object has mass 35.1 g and volume 27 cm³. Find its density.

   Formula:Density

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

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7. 7.

   A wave has frequency 818 Hz and wavelength 0.47 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A circle has a radius of 22 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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9. 9.

   ₽2,500 is invested at 6% compound interest per annum for 5 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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10. 10.

    A force of 310 N acts on an area of 5.7 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A right-angled triangle has legs of 8 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    A force of 460 N acts on an area of 7.1 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Find the force needed to accelerate a 19 kg mass at 8.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A cone has base radius 11 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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15. 15.

    A right-angled triangle has legs of 4 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A value changes from 199 to 247. 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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17. 17.

    A force of 88 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    Find the force needed to accelerate a 34 kg mass at 3.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A circle has a radius of 18 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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20. 20.

    A car travels 237 km in 3 hours. Find its average speed.

    Formula:Speed

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

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