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The length, breadth and height of a cuboidal room are in the ratio 20 : 12 : 9. If the area of four walls of room is 2304 cm2 then find the total surface area of a cube whose side length is equal to the height of cuboid.

The length, breadth and height of a cuboidal room are in the ratio 20 : 12 : 9. If the area of four walls of room is 2304 cm2 then find the total surface area of a cube whose side length is equal to the height of cuboid. Correct Answer 1944 cm<sup>2</sup>

Given:

The length, breadth and height of a cuboidal room are in the ratio 20 : 12 : 9

The area of four walls of room is 2304 cm2

Formula used:

Area of four walls of cuboid = 2 (l + b) × h

Total surface of cube = 6a2

Calculation:

Let the ratio be x

So, length of cuboid = 20x

Breath of cuboid = 12x

Height of cuboid = 9x

Since, Area of four walls of cuboid = 2 (l + b) × h

2304 = 2 (20x + 12x) × 9x

⇒ 576x2 = 2304

⇒ x2 = 4

So, x = + 2 or x = – 2 (not possible)

So, length = 20 × 2 = 40cm

Breadth = 12 × 2 = 24cm

And height = 9 × 2 = 18cm

According to question,

Side of cube = height of cuboid = 18cm

So, total surface area of cube = 6 × (18)2 cm2

Hence, 1944 cm2

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