# Cuboid

Last Updated : 13 Nov, 2023

Cuboid verbal reasoning questions: A cuboid is a rectangular solid with six rectangular faces, where each pair of opposite faces is congruent (equal in size) and parallel to each other. A cuboid is also known as a rectangular prism or rectangular parallelepiped.

Key characteristics of a cuboid include:

1. Six faces: A cuboid has six faces, and each face is a rectangle.
2. Twelve edges: It has twelve edges or straight lines where two faces meet.
3. Eight vertices: A cuboid has eight corners or vertices.

Cuboids are commonly encountered in geometry, and understanding their properties is essential for solving problems related to spatial reasoning and visualization. In logical reasoning tests, cuboids may be used as a part of geometric or spatial reasoning questions, where test-takers are asked to make deductions, comparisons, or inferences based on the properties and relationships of cuboids.

## Cuboid – Solved Examples

Question 1:

A cuboid has dimensions of 10 cm, 12 cm, and 15 cm. What is the length of the longest diagonal of the cuboid?

(a) 27 cm (b) 37 cm (c) 39 cm (d) 42 cm

Answer: (d) 42 cm

The longest diagonal of a cuboid is formed by joining two opposite corners. Using the Pythagorean theorem, we can find the length of this diagonal as:

102+122+152â€‹=625â€‹=255â€‹=42 cmâ€‹

Question 2:

A cuboid has a volume of 960 cmÂ³. If the length and width of the cuboid are 12 cm and 8 cm, respectively, what is the height of the cuboid?

(a) 10 cm (b) 12 cm (c) 15 cm (d) 20 cm

Answer: (a) 10 cm

The volume of a cuboid is given by:

Volume=lengthÃ—widthÃ—height

Substituting the given values, we get:

960=12Ã—8Ã—height

Solving for height, we get:

height=12Ã—8960â€‹=10 cm

Question 3:

A cuboid has a surface area of 1200 cmÂ². If the length and width of the cuboid are 10 cm and 12 cm, respectively, what is the height of the cuboid?

(a) 10 cm (b) 12 cm (c) 15 cm (d) 20 cm

Answer: (c) 15 cm

The surface area of a cuboid is given by:

Surface Area=2(lengthÃ—width+widthÃ—height+lengthÃ—height)

Substituting the given values, we get:

1200=2(10Ã—12+12Ã—height+10Ã—height)

Solving for height, we get:

height=2(12+10)1200âˆ’2(10Ã—12)â€‹=15 cm

Question 4:

A cuboid has a length of 15 cm, a width of 10 cm, and a height of 8 cm. How many smaller cubes with a side length of 2 cm can fit inside the cuboid?

(a) 120 (b) 240 (c) 360 (d) 720

Answer: (c) 360

To determine the number of smaller cubes that can fit inside the cuboid, we need to divide the dimensions of the cuboid by the side length of the smaller cube:

Number of cubes=215â€‹Ã—210â€‹Ã—28â€‹=360

Question 5:

A cuboid has a length of 20 cm, a width of 15 cm, and a height of 12 cm. What is the ratio of the surface area of the cuboid to the volume of the cuboid?

(a) 1:10 (b) 2:15 (c) 3:20 (d) 4:25

Answer: (d) 4:25

The surface area of a cuboid is given by:

Surface Area=2(lengthÃ—width+widthÃ—height+lengthÃ—height)

Substituting the given values, we get:

Surface Area=2(20Ã—15+15Ã—12+20Ã—12)=1260 cm2

The volume of a cuboid is given by:

Volume=lengthÃ—widthÃ—height

Substituting the given values, we get:

Volume=20Ã—15Ã—12=3600 cm3

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