India · Class 10 · Practice Sheet 9

1. 1.

   A cylinder has radius 6 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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2. 2.

   A device runs at 130 V drawing 5.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A bag has 19 equally likely marbles, of which 10 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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4. 4.

   Find the gravitational potential energy of a 45 kg object raised 25 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   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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6. 6.

   Solve for x: 8x + 11 = 51.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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7. 7.

   Find the momentum of a 50 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A force of 62 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A wave has frequency 253 Hz and wavelength 3.13 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    In a triangle, a = 7, b = 13 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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11. 11.

    A bag has 11 equally likely marbles, of which 1 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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12. 12.

    A force of 119 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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13. 13.

    A wave has frequency 563 Hz and wavelength 4.28 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A cone has base radius 10 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    An object with initial velocity 6 m/s accelerates at 1.7 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    Find the gravitational potential energy of a 45 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A value changes from 81 to 185. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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18. 18.

    Solve for x: 4x + 15 = 23.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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19. 19.

    A bag has 22 equally likely marbles, of which 3 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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20. 20.

    An object has mass 108 g and volume 12 cm³. Find its density.

    Formula:Density

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

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