Volume and Surface Area of Cuboid

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Volume and Surface Area of Cuboid Definitions

Volume of a Cuboid: The volume of a cuboid is nothing but the space occupied by the object. The volume of a cuboid is the product of three dimensions length, breadth, and height. The volume of a cuboid depends on the length of the edge. The metric units of volume of the cuboid are cubic units.

Surface Area of a Cuboid: A surface area of a cuboid is the total amount of space occupied by the solid shape. It has three dimensions length, breadth, and height. The metric units of the surface area of the cuboid are square units, square cm, square meters, square inches.

What is Cuboid?

A Cuboid is a 3D figure that contains six faces, eight vertices, and twelve edges. It has a square surface and a rectangular surface. The shape of cuboid and cube are mostly the same but have different properties. The volume and surface area of cuboid and cube are different from each other.

cuboid

Surface Area and Volume of Cuboid Formula

Volume:
Volume of cuboid = l × b × h

Surface area formula:
Total surface Area of a Cuboid (S) = 2(lb + bh +hl)
Diagonal of a Cuboid (d) =√ l2+b2+h2
Where
l = length
b = breadth
h = height

How to Find Volume and Surface Area of Cuboid?

Follow the below steps to find the surface area and volume of a cuboid.

  1. First, you have to check out the given three-dimensional figure whether it is a cuboid or not.
  2. Now, see what we have to find from the given question.
  3. Apply the related formula to find the area or volume of the cuboid.
  4. And then write the obtained result and write the units with the answer.

Volume and Surface Area of Cuboid Questions

Example 1.
The cuboid has three mutually perpendicular edges measuring 5 cm, 6 cm, and 7 cm. Find its volume, surface area, and length of the diagonal.
Solution:
Three mutually perpendicular edges are length, breadth and height.
cuboid_12
Length = 5 cm
breadth = 6 cm
height = 7 cm.
Volume of cuboid = l × b × h
5 × 6 × 7 cm³
210 cm³
Surface area = 2(lb + bh + hl)
2(5 × 6 + 6 × 7 + 7 × 5)
= 214
Length of a diagonal =√ l2+b2+h2
= √(5)² + (6)² + (7)²
= √ 25 + 36 + 49
= 10.48 cm
Thus the length of a diagonal is 10.48 cm.

Example 2.
The length, breadth, and volume of a cuboid are 6 cm, 3 cm, and 80 cm³ respectively. Find its height, surface area.
Solution:
Given that
cuboid_13
Length = 6
breadth = 3
Volume = 80
height = h.
volume of a cuboid = l × b × h
80 cm³ = 6 cm × 3 cm × h
h = 80 cm³/6 cm × 3 cm
h = 80cm³/18 cm²
h = 4.4 cm.
Therefore, height = 4.4 cm.
Surface area = 2(lb + bh + hl)
= 2(6 × 3 + 3 × 4.4 + 4.4 × 6) cm²
= 2(18 + 13.2 + 26.4) cm²
= 2(115.2) cm²
= 115.2 cm²
Thus the surface area is 115.2 cm²

Example 3.
The dimensions of a cuboid are 13, 14, 16. Then find the volume and surface area.
Solution:
Given that
cuboid_14
Length = 13 cm
breadth = 14 cm
Height = 16 cm.
Volume of a cuboid = l × b × h
= 13 × 14 × 16
= 2912
The total surface area = 2 (lb + bh + hl)
=2((13 ×14) + (14×16) + (16×13)
= 2(182 + 224 + 208)
= 2(614) cm²
= 1228 cm²
Therefore, the total surface area of a cuboid= 1228 cm²

Example 4.
The dimensions of a cuboid are 3, 4, 6. Then find the volume and surface area.
Solution:
Given that
cuboid_15
Length = 3 cm
breadth = 4 cm
Height = 6 cm.
Volume of a cuboid = l × b × h
= 3 × 4 × 6
= 72
The total surface area = 2 (lb + bh + hl)
=2((3 ×4) + (4×6) + (6×3)
= 2(12 + 24 + 18)
= 2(54) cm²
= 108 cm²
Therefore, the total surface area of a cuboid= 108 cm²

Example 5.
The length, breadth, and volume of a cuboid are 5 cm, 10 cm, and 60 cm³ respectively. Find its height, surface area.
Solution:
Given that
cuboid_16
Length = 5
breadth = 10
Volume = 60
height = h.
volume of a cuboid = l × b × h
60 cm³ = 5 cm × 10 cm × h
h = 60 cm³/5 cm × 10 cm
h = 60cm³/15 cm²
h = 4 cm.
Therefore, height = 4 cm.
Surface area = 2(lb + bh + hl)
= 2(5 × 10 + 10 × 4 + 4 × 5) cm²
= 2(50 + 40 + 25) cm²
= 2(115) cm²
= 230 cm²
Thus the surface area is 230 cm²

FAQs on Volume and Surface Area of Cuboid

1. What is the formula of the surface area of a cuboid?

To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length, width, and height of the prism and use the formula, SA=2lw + 2lh + 2hw, to find the surface area.

2. What is the formula of volume of cuboids?

The formula of volume of a cuboid is = Length × Width × Height.

3. How do you work out the volume of a cuboid in Litres?

Volume of a cuboid = (length × breadth × height) cubic units. = (l × b × h) cubic units.

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