Examples on Cuboid
Example 1: Find the height of a cuboid given that its total surface area is 108 sq. units, length 4 units, and breadth 6 units.
Solution:
Let the height be h units
Given,
- Total Surface Area(a) = 108 sq. units
- Length(l) = 4 units
- Breadth(b) = 6 units
We know, h = (a – 2.lb)/{2(l + b)}
⇒ h = {108 – 2.(4)(6)}/{2.(4 + 6)} = 60/20
⇒ h = 3 units
Example 2:Determine the lateral surface area of a cuboid if its length, breadth, and height are 15 in, 8 in, and 12 in, respectively.
Solution:
Given,
- Length of a cuboid (l) = 15 in
- Breadth of a cuboid (b) = 8 in
- Height of a cuboid (h) = 12 in
We have,
Lateral Surface Area of a Cuboid(A) = 2h(l + b)
A = 2 × 12 (15 + 8)
A = 24 × 23 = 552 square inches.
Hence, lateral surface area of the given cuboid is 552 square inches.
Example 3: Robert has to cover the edges of a rectangular box with a tape. How much minimum tape does he require if the dimensions of the cuboid are 16 in × 10 in × 8 in?
Solution:
Since Robert has to cover the edges of a box, so he has to find the perimeter of the box i.e., cuboid.
Given,
- Length of a cuboid (l) = 16 in
- Breadth of a cuboid (b) = 10 in
- Height of a cuboid (h) = 8 in
Perimeter of Cuboid(P) = 4(l + w + h)
P = 4(16 + 10 + 8) = 4 × 34 = 136 inches
Hence, the minimum tape required to cover the edges of a rectangular box with a tape is 136 inches.
Example 4: If the length and width of a cuboid are 6 inches and 8 inches respectively, what will be the value of face diagonal?
Solution:
Given,
- Length of a cuboid (l) = 6 in
- Width of a cuboid (w) = 8 in
Face Diagonal(d) = √(l2 + w2)
d = √(62 + 82) = √(100) = 10 inches
Hence, the value of face diagonal of the cis 10 inches.
Example 5: Determine the length and the total surface area of a cuboid whose lateral surface area is 960 sq. in and whose breadth and height are 12 in and 16 in, respectively.
Solution:
Given,
- Breadth of a Cuboid (b) = 12 in
- Height of a Cuboid (h) = 16 in
- Lateral Surface Area = 960 square inches
We know that,
Lateral Surface Area of Cuboid(LSA) = 2h(l + b)
⇒ 2 × 16 (l + 12) = 960
⇒ 32 (l + 12) = 960
⇒ (l + 12) = 960/32 = 30
⇒ l = 30 – 12 = 18 in
We have,
Total Surface Area of Cuboid(TSA) = 2 (lb + bh + lh)
TSA = 2 [(18 × 12) + (12 × 16) + (18 × 16)] = 2 [ 216 + 192 + 288]
TSA = 2 × [696] = 1398 square inches
Hence, length and total surface area of cuboid are 18 in and 1398 sq. in, respectively.
Cuboid – Shape and Properties
Cuboid is a three-dimensional shape that looks like a rectangular box in our everyday life. Cuboids have 6 faces, 12 edges, and 8 vertices. A cuboid is also called a rectangular prism. Example of a cuboid in real life is a shoe box.
In this article, we will learn about all things cuboid such as definition, shape, dimensions, and others in detail.
Table of Content
- What is Cuboid?
- Shape of a Cuboid
- Dimensions of a Cuboid
- Faces, Edges and Vertices of a Cuboid
- Diagonals of a Cuboid
- Properties of a Cuboid
- Cuboid Formula
- Surface Area of Cuboid
- Volume of Cuboid
- Net of Cuboid
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