Taiwan · Grade 12 · Practice Sheet 22

1. 1.

   A cone has base radius 2 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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2. 2.

   Find the momentum of a 36 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   Two masses 5,300 kg and 630 kg are 9 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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4. 4.

   A force of 28 N acts on an area of 6.9 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A force of 13 N moves an object 3 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   In a triangle, a = 11, b = 14 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   NT$ 3,400 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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8. 8.

   A force of 106 N moves an object 2 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   In a triangle, a = 6, b = 13 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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10. 10.

    A force of 221 N acts on an area of 9.2 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    In a triangle, a = 7, b = 14 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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12. 12.

    A force of 24 N moves an object 40 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    Find the force needed to accelerate a 17 kg mass at 8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the momentum of a 33 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    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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16. 16.

    In a triangle, a = 8, b = 6 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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17. 17.

    Find the gravitational potential energy of a 31 kg object raised 21 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Two masses 7,600 kg and 700 kg are 17 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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19. 19.

    Find the momentum of a 3 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A cone has base radius 5 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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