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A cuboid has total surface area of $50 m 2$ and lateral surface area of $30 m 2$ . Find the area of its base.

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20 m 2

10 m 2

30 m 2

40 m 2

answer is B.

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Detailed Solution

It is given a cuboid has total surface area of

50 m 2

and lateral surface area of

30 m 2

. The total surface area of a cuboid is,

⇒ T . S . A = 2 (l b + b h + h l)

… (1)
The lateral surface area of a cuboid is,

⇒ L . S . A = 2 (b h + h l)

… (2)
Equate the values of total and lateral surface areas with the formula.
Since, the total surface area of a cuboid is

50 m 2

⇒ T . S . A = 50 m 2

Substitute the value of T.S.A from equation

1

⇒ 2 (l b + b h + h l) = 50

… (3)
Since, the lateral surface area of a cuboid is

30 m 2

⇒ L . S . A = 30 m 2

Substitute the value of L.S.A from equation

2

⇒ 2 (b h + h l) = 30 … (4)

Subtract L.S.A from T.S.A.
Subtract equation (4) from equation

3

⇒ 2 (l b + b h + h l) − 2 (b h + h l) = 50 − 30

⇒ 2 l b + 2 b h + 2 h l − 2 b h − 2 h l = 20

⇒ 2 l b = 20

Dividing both sides by

2

⇒ 2 l b 2 = 202

⇒ l b = 10

… (5)
Since, the base of cuboid has dimensions’ length and breadth.

⇒

Area of base of cuboid is

l × b

.
Substitute the value of the product from the equation

5

⇒

The area of the base of the cuboid is

10 m 2

.
Hence option (2) is correct,

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