Egypt · Grade 11 · Practice Sheet 32

1. 1.

   A right-angled triangle has legs of 13 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A cylinder has radius 14 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   Find the gravitational potential energy of a 47 kg object raised 8 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A right-angled triangle has legs of 3 cm and 5 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   A cone has base radius 12 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   Two masses 5,100 kg and 830 kg are 3 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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8. 8.

   An object has mass 41.4 g and volume 9 cm³. Find its density.

   Formula:Density

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

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9. 9.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    A device runs at 66 V drawing 8.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the momentum of a 31 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A 16 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    Two masses 4,100 kg and 670 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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14. 14.

    Find the force needed to accelerate a 37 kg mass at 7.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the momentum of a 4 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A body starts at 1 m/s and accelerates at 5.9 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    An object with initial velocity 12 m/s accelerates at 3.7 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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18. 18.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 9 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    In a triangle, a = 10, b = 15 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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20. 20.

    A device runs at 75 V drawing 5.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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