Question

The length breadth and height of a cuboid are in the ratio 5:3:2, and its total area is 3968 cm2. Find the dimensions of the cuboid.​

Answer 1

Step-by-step explanation:

Let the length, breadth and height of the cuboid be 5x,3x and 2x respectively.

We know that the volume of the cuboid is l×b×h.

It is given that the volume of the cuboid is 35.937 m

3

, therefore,

35.937=5x×3x×2x

⇒30x

3

=35.937

⇒x

3

=

30

35.937

=1.197

⇒x=

3

1.197

⇒x=0.33

Therefore, the length l=5x=5×0.33=1.65, breadth b=3x=3×0.33=0.99 and height h=2x=2×0.33=0.66

Now, the total surface area of cuboid is 2(lb+bh+hl), therefore, the total surface area with length 1.65 m, breadth 0.99 m and height 0.66 m is:

A=2[(1.65×0.99)+(0.99×0.66)+(0.99×1.65)]=2(1.6335+0.6534+1.089)=2×3.3759=6.7518 m

2

Hence, the dimensions of cuboid is 1.65 m, 0.99 m and 0.66 m and the total surface area of cuboid is 6.7518 m

2

.