Russia · Grade 11 · Practice Sheet 45

1. 1.

   A cone has base radius 5 cm and height 5 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.

   An object with initial velocity 9 m/s accelerates at 4.2 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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3. 3.

   ₽2,600 is invested at 3% 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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4. 4.

   A cone has base radius 4 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   A right-angled triangle has legs of 17 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   Find the momentum of a 15 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   An object has mass 146.2 g and volume 43 cm³. Find its density.

   Formula:Density

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

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8. 8.

   Find the gravitational potential energy of a 4 kg object raised 8 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Find the force needed to accelerate a 44 kg mass at 2.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Two masses 5,400 kg and 300 kg are 2 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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11. 11.

    A cone has base radius 3 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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12. 12.

    A triangle has sides a = 20 cm and b = 17 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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13. 13.

    ₽700 is invested at 4% compound interest per annum for 2 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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14. 14.

    A force of 51 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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15. 15.

    A cone has base radius 11 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    A force of 56 N acts on an area of 5.8 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the momentum of a 9 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    In a triangle, a = 16, b = 7 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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19. 19.

    Find the momentum of a 20 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A force of 92 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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