Czechia · Grade 11 · Practice Sheet 47

1. 1.

   A cylinder has radius 14 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   An object has mass 66 g and volume 11 cm³. Find its density.

   Formula:Density

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

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3. 3.

   A current of 7.6 A flows through a 40 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   A cylinder has radius 13 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   Find the momentum of a 7 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A force of 310 N acts on an area of 4.5 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

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

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   A cone has base radius 9 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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10. 10.

    A force of 90 N acts on an area of 0.7 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A cylinder has radius 4 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    Solve using the quadratic formula: x² − 5x + 4 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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13. 13.

    A cylinder has radius 2 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    A current of 2.2 A flows through a 20 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    Solve using the quadratic formula: x² + 1x + 0 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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16. 16.

    A device runs at 208 V drawing 9.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    In a triangle, a = 10, b = 15 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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18. 18.

    Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 3.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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19. 19.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 7 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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20. 20.

    A wave has frequency 837 Hz and wavelength 2.13 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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