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:
- Six faces: A cuboid has six faces, and each face is a rectangle.
- Twelve edges: It has twelve edges or straight lines where two faces meet.
- Eight vertices: A cuboid has eight corners or vertices.
Cuboid - Solved Examples
Question 1: A cuboid has dimensions of 9 cm, 12 cm, and 20 cm. What is the length of the longest diagonal of the cuboid?
(a) 15 cm (b) 25 cm (c) 35 cm (d) 5 cm
Using the space diagonal formula:
d=\sqrt{l^2+b^2+h^2}
=\sqrt{9^2+12^2+20^2} = \sqrt{625} d = 25cm
Question 2: A cuboid has a volume of 960 cm³. 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
The volume of a cuboid is given by: Volume = length × width × height
Substituting the given values, we get:
960 = 12 × 8 × height
Solving for height, we get: height = 960/96 = 10 cm
Question 3: A cuboid has a surface area of 900 cm². 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
The surface area of a cuboid is given by:
Surface Area = 2(length × width + width × height + length × height)
Substituting the given values, we get:
900 = 2(10×12+12h+10h)
450 = 120+22h
22h = 330
h = 15
Question 4: A cuboid has a length of 18 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) 180 (c) 360 (d) 720
Number of cubes =
\frac{18}{2}\times \frac{10}{2} \times \frac{8}{2} 9 ⨉ 5 ⨉ 4 = 180
Question 5: A cuboid has a length of 20 cm, a width of 10 cm, and a height of 5 cm. What is the ratio of the surface area to itsvolume?
(a) 11:10 (b) 7:10 (c) 10:7 (d) 10:1
Surface area: =2(lb + bh + lh)
=2(20 × 10 + 10 × 5 + 20 × 5)
=2(200 + 50 +1 00) = 700 cm2
Volume: = 20 × 10 × 5 = 1000 cm3
Ratio: 700:1000 = 7:10