Question

The length, breadth and height of a cuboid are in the ratio 6 : 5 : 4. If its volume is 15,000 cubic cm.; Find its dimensions.​

Answer 1

Answer:

Let the dimensions of the cuboid be 6x, 5x, and 4x.

According to the problem

volume of the cuboid= length ×breadth ×height

6x×5x×4x= 15000

120x^3=15000

x^3= 125

x=5

Therefore, the dimensions are 30cm, 25cm and 20cm.

Answer 2

Answer:

Let the length of the cuboid =6x, breadth =5x, height =3x

Total surface area of a cuboid of length l, breadth b and height h

=2(l×b+b×h+l×h)

Given, total surface area of the cuboid =504cm

2

2(6x×5x+5x×3x+6x×3x)=504cm

2

126x

2

=504

=>x=2

Hence, the length of the cuboid =6x=12cm, breadth =5x=10cm, height =3x=6cm

Volumeof a cuboid of length l, breadth b and height h =l×b×h

So, the volume of the cuboid with length =12cm, breadth =10cm and height =6cm=12×10×6=720cm

3