Russia · Grade 10 · Practice Sheet 20

1. 1.

   A cone has base radius 2 cm and height 16 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.

   ₽2,000 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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3. 3.

   A cone has base radius 5 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   A wave has frequency 41 Hz and wavelength 3.48 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A cylinder has radius 13 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   Solve for x: 3x + 14 = 38.

   Formula:Solving a Linear Equation

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

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7. 7.

   Find the gravitational potential energy of a 43 kg object raised 18 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   A value changes from 196 to 235. 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.

   ₽2,300 is invested at 10% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

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

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10. 10.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    A body starts at 17 m/s and accelerates at 3.6 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    An object has mass 96.2 g and volume 37 cm³. Find its density.

    Formula:Density

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

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13. 13.

    Find the momentum of a 23 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    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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15. 15.

    A force of 249 N acts on an area of 9.2 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A 5 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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17. 17.

    A right-angled triangle has legs of 19 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    Find the momentum of a 7 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A force of 45 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Solve for x: 7x + 20 = 55.

    Formula:Solving a Linear Equation

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

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