Ireland · Year 11 · Practice Sheet 50

1. 1.

   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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2. 2.

   A population of 6,000 grows 10% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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3. 3.

   Find the momentum of a 7 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A force of 448 N acts on an area of 2.4 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   An object has mass 191.4 g and volume 33 cm³. Find its density.

   Formula:Density

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

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6. 6.

   A 6 kg object moves at 19 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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7. 7.

   A wave has frequency 34 Hz and wavelength 4.29 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Two masses 7,500 kg and 660 kg are 16 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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9. 9.

   A cone has base radius 8 cm and height 6 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.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 6 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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11. 11.

    A population of 5,700 grows 2% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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12. 12.

    A right-angled triangle has legs of 5 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    A cylinder has radius 10 cm and height 18 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 3.2 A flows through a 26 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    An object has mass 35.7 g and volume 21 cm³. Find its density.

    Formula:Density

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

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16. 16.

    A population of 7,500 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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17. 17.

    A cylinder has radius 6 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    A cone has base radius 3 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    A device runs at 60 V drawing 0.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the momentum of a 3 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

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