Bangladesh · Class 11 · Practice Sheet 28

1. 1.

   Find the volume of a sphere of radius 12 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 4,800 grows 2% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A cylinder has radius 12 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   A population of 8,500 grows 5% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   A force of 111 N moves an object 18 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A device runs at 175 V drawing 6.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the force needed to accelerate a 53 kg mass at 0.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A right-angled triangle has legs of 8 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   An object with initial velocity 3 m/s accelerates at 3.6 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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10. 10.

    In a triangle, a = 13, b = 17 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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11. 11.

    A force of 17 N moves an object 12 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    An object with initial velocity 13 m/s accelerates at 1.8 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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13. 13.

    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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14. 14.

    Find the gravitational potential energy of a 32 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A wave has frequency 499 Hz and wavelength 2.54 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Solve using the quadratic formula: x² − 2x − 24 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    Two masses 2,500 kg and 530 kg are 5 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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18. 18.

    Find the momentum of a 58 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    In a triangle, a = 16, b = 17 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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20. 20.

    A triangle has sides a = 8 cm and b = 14 cm with an included angle C = 90°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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