Italy · Classe 10 · Practice Sheet 49

1. 1.

   A cone has base radius 8 cm and height 16 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 force of 58 N moves an object 13 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A current of 1.5 A flows through a 26 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the gravitational potential energy of a 13 kg object raised 11 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A 35 kg object moves at 6 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   A cone has base radius 12 cm and height 16 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.

   A right-angled triangle has legs of 9 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   A triangle has sides a = 14 cm and b = 14 cm with an included angle C = 60°. 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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9. 9.

   A wave has frequency 55 Hz and wavelength 3.43 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    €3,100 is invested at 3% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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11. 11.

    Find the gravitational potential energy of a 27 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A force of 58 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 force of 131 N acts on an area of 3.7 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    €2,900 is invested at 8% compound interest per annum for 3 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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15. 15.

    Find the force needed to accelerate a 8 kg mass at 6.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    A body starts at 0 m/s and accelerates at 1.7 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A device runs at 154 V drawing 7.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Solve using the quadratic formula: x² − 5x + 6 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    Find the force needed to accelerate a 30 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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