Question

The length, breadth and height of a room are 6 m, 4 m and 5 m respectively. The room
holds 250 boxes. If all the dimensions of the room are doubled, the number of beres
it will hold (boxes of the same size)
​

Answer 1

ANSWER :-

• 1920 Boxes.

GIVEN :-

• Dimensions of room are 6m , 4m and 5m.
• The room holds 250 boxes.

TO FIND :-

• Number of boxes of same volume the room can bear if the dimensions of the room are doubled.

TO KNOW :-

★ Volume of Cuboid = l × b × h

Here ,

• l = Length
• b = Breadth
• h = Height

SOLUTION :-

As 250 boxes are placed in the room ,

Volume of 250 boxes = Volume of room

250 × Volume of one box = Volume of room

250 × Volume of one box = 6 × 5 × 4

250 × Volume of one box = 120

Volume of one box = 120/250

Volume of one box = 12/25 cm³

Now , we will double the dimensions of the room.

New dimensions ,

• l = 2 × 6 = 12cm
• b = 2 × 4 = 8cm
• h = 2 × 5 = 10cm

Now again ,

Volume of new room = Volume of Total boxes

Let the total number of boxes be 'p'.

→ Volume of new room = p × Volume of one box

We know , volume of one box = 12/25 cm³

Putting values , we get...

→ 12 × 8 × 10 = p × (12/25)

→ 960 = p × (12/25)

→ p = 960 × (24/12)

→ p = 23040/12

→ p = 1920

Hence , 1920 boxes can be placed if the dimensions of the room are doubled.

MORE TO KNOW :-

★ Volume of cube = edge³

★ Volume of cylinder = πr²h

★ Volume of cone = (1/3)πr²h

★ Volume of hemisphere = (2/3)πr³

★ Volume of sphere = (4/3)πr³