Pakistan · Class 10 · Practice Sheet 30

1. 1.

   A cone has base radius 6 cm and height 18 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.

   A wave has frequency 693 Hz and wavelength 2.45 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 11 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   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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5. 5.

   ₨1,700 is invested at 8% compound interest per annum for 4 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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6. 6.

   Find the gravitational potential energy of a 50 kg object raised 36 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Find the force needed to accelerate a 2 kg mass at 0.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A value changes from 196 to 114. 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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9. 9.

   An object has mass 26 g and volume 26 cm³. Find its density.

   Formula:Density

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

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10. 10.

    Find the momentum of a 48 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A cone has base radius 4 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    A body starts at 12 m/s and accelerates at 5 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A 14 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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14. 14.

    An object has mass 54.6 g and volume 7 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A force of 251 N acts on an area of 3 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A body starts at 9 m/s and accelerates at 1.7 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    Find the momentum of a 23 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 11 N moves an object 35 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A cylinder has radius 2 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A force of 33 N acts on an area of 1.6 m². Find the pressure.

    Formula:Pressure

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

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