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The lateral surface area and the total surface area of a cuboid of dimensions $40 cm × 30 cm × 20 cm$ are $c m 2$ and $c m 2$ respectively.

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Detailed Solution

The lateral surface area and the total surface area of a cuboid of dimensions

40 cm × 30 cm × 20 cm

are

2800 cm 2

and

5200 cm 2

respectively.
Given that,
Length of a cuboid = 40 cm.
Breadth of a cuboid = 30 cm.
Height of a cuboid = 20 cm.
We know that the lateral surface area of a cuboid is

2 l + b × h .

The total surface area of a cuboid is

2 l b + b h + l h .

where

l

is the length of the cuboid,

b

is the breadth, and

h

is the height.
Calculate the lateral surface area as shown,

L S A = 2 l + b × h = 2 40 + 30 × 20 = 2800 cm 2

Calculate the total surface area as shown,

T S A = 2 l b + b h + l h = 2 40 × 30 + 30 × 20 + 40 × 20 = 2 1200 + 600 + 800 = 2 × 2600 = 5200 cm 3

Therefore, the lateral surface area of a cuboid is

2800 cm 2

and total surface area of the cuboid is

5200 cm 2 .

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