Mathematics: Cuboid Formation with Equal Cubes

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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?

A tall and thin cylindrical shape. 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?

Box B Signup and view all the answers

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

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

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

$2h(l + b)$ 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?

Remain the same Signup and view all the answers

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

Lateral surface area + 2 times the base area Signup and view all the answers

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

Directly proportional to both length and width Signup and view all the answers

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

$2(h + l + b)$ 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?

No, only in some cases Signup and view all the answers

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

$l \times b \times h$ 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?

5 Signup and view all the answers

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

Cube 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?

100 cubic units Signup and view all the answers

Which geometric property does a cube exhibit?

All angles are right angles 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?

$72 , cm^2$ Signup and view all the answers