Mathematics: Cuboid Formation with Equal Cubes
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Mathematics: Cuboid Formation with Equal Cubes

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Questions and Answers

Can the volume of a cylinder be calculated by multiplying the area of its base by its height?

  • No, because the volume of a cylinder is not related to the area of its base.
  • Yes, because the top and base of a cylinder are congruent and parallel to each other.
  • No, because a cylinder has curved surfaces that affect the volume calculation differently. (correct)
  • Yes, because the lateral surface of a cylinder is perpendicular to the base.

    • If two cuboids have the same volume, can they have different total surface areas?

  • Yes, because total surface area depends on the dimensions of the cuboid. (correct)
  • No, because same volume implies same surface area.
  • No, because total surface area is directly proportional to volume.
  • Yes, because total surface area is not related to volume.

    • What is used to calculate the total surface area of a cuboid?

  • The length and width of the base only.
  • The length and height of the cuboid only.
  • The product of all three dimensions.
  • The sum of areas of all its faces. (correct)

    • Which shape could have the greatest surface area for a given volume?

    <p>A tall and thin cylindrical shape.</p> Signup and view all the answers

    If a cuboidal box A has dimensions 3cm x 8cm x 20cm, and box B has dimensions 4cm x 12cm x 10cm, which box would be more economical to the company for packing biscuits?

    <p>Box B</p> Signup and view all the answers

    Can two solid shapes with different volumes have the same total surface area?

    <p>Yes, because total surface area depends on shape and dimensions, not volume.</p> Signup and view all the answers

    What formula can be used to find the lateral surface area of a cuboid?

    <p>$2h(l + b)$</p> Signup and view all the answers

    If the lengths of the base and the height of a cuboid are interchanged, what will happen to the lateral surface area?

    <p>Remain the same</p> Signup and view all the answers

    What is the total surface area of a cuboid equal to?

    <p>Lateral surface area + 2 times the base area</p> Signup and view all the answers

    How is the lateral surface area of a cuboid related to its dimensions?

    <p>Directly proportional to both length and width</p> Signup and view all the answers

    What formula can be used to find the total surface area of a cuboid?

    <p>$2(h + l + b)$</p> Signup and view all the answers

    Can we say that the total surface area of a cuboid is always equal to its lateral surface area plus twice the base's area?

    <p>No, only in some cases</p> Signup and view all the answers

    What is the formula to find the volume of a cuboid?

    <p>$l \times b \times h$</p> Signup and view all the answers

    In the context of forming a cuboid with cubes, if the length is 4 and breadth is 3, what could be the possible value for height?

    <p>5</p> Signup and view all the answers

    What is the special case of a cuboid where the length, breadth, and height are all equal?

    <p>Cube</p> Signup and view all the answers

    If the base of a cuboid has an area of 20 square units and the height is 5 units, what is the volume of the cuboid?

    <p>100 cubic units</p> Signup and view all the answers

    Which geometric property does a cube exhibit?

    <p>All angles are right angles</p> Signup and view all the answers

    If a cuboid has dimensions of 6 cm, 4 cm, and 3 cm, what is its total surface area?

    <p>$72 , cm^2$</p> Signup and view all the answers

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