How many small cubes of lateral surface area 16 cm2 can be made by a cuboidal box whose length, breadth and height are in the ratio 15 ∶ 12 ∶ 8 and the lateral surface area of cuboid is 432 cm2. ?

160
165
175
180

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 4 : 180

Calculation:

Let the ratio be x

So, length = 15x

Breadth = 12x

And height = 8x

According to question,

Lateral surface area = 432 cm²

2 (l + b) × h = 432

⇒ 2 (15x + 12x) × 8x = 432

⇒ 432x²= 432

So, x = 1

So, the volume of cuboid = 15x × 12x × 8x = 1440x³= 1440 cm³

Now, lateral surface area of cube = 16 cm²

4a²= 16

⇒ a = 2

Volume of cube = 2³= 8 cm³

So, the number of small cubes = 1440/8

Hence, 180

4 views Answered 2022-09-04 04:29

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