Question

the length , width and height of a hail are in the ratio 8:6:3 . if the volume is 18000m³ found the dimensions of the room
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Answer 1

Correct Question :

The length, width and height of a hall are in the ratio 8 : 6 : 3 . if the volume is 18000m³. Find the dimensions of the room.

Answer :

The dimensions of the room is 40m × 30m × 15m

Step-by-step explanation :

To Find,

• The dimensions of the room

Solution,

Given that,

• The length, width and height of a hall are in the ratio 8:6:3
• The volume is 18000 m³

Therefore,

Let us assume the lenght, breadth and height as 8x, 6x and 3x respectively.

As we know that,

Volume of cuboid = ( l × b × h )

Where,

• l = Length
• b = Breadth
• h = height

➮ 18000 = ( 8x × 6x × 3x )

➮ 18000 = ( 48x² × 3x )

➮ 18000 = 144x³

➮ x³ = 18000 / 144

➮ x³ = 125

➮ x³ = 5 × 5 × 5

➮ x = 5

The value of x is 5.

Therefore, the dimensions of the room is,

• Length ( we assumed lenght as 8x )

➮ 8x

➮ 8 × 5

➮ 40 m

• Breadth ( we assumed breadth as 6x )

➮ 6x

➮ 6 × 5

➮ 30 m

• Height ( we assumed height as 3x )

➮ 3x

➮ 3 × 5

➮ 15 m

The dimensions of the room is 40m × 30m × 15m.