Question

The breadth of a box is twice its height and half its length. The volume of room is 512 cubic cm. find the length of box?​

Answer 1

Here given that breadth of a box is twice its height & half its length.Volume of cuboid room is 512 cm³.

We have to find length of box.

Solution:-

Case 1 :

→ Breadth = 2 × Height

→ Breadth = ½ × Length ---- Equation (1)

So, 2 × Height = ½ × Length

→ Height = (½ × Length)/2

→ Height = Length/4 ---- Equation (2)

As we know,

→ Volume of cuboid = l × b × h

Putting Values from Equation 1 & 2 :

→ 512 = length × (length /2) × (length /4)

→ 512 = (Length³)/8

→ Length³ = 512 × 8

→ Length³ = 4096

Cubing root on both sides :

→ ³√Length = ³√4096

→ Length = 16 cm

Therefore,

∴ Length of box = 16 cm.

Answer 2

Step-by-step explanation:

Given -

• Breadth of a box is twice its height and Half its length
• Volume of room is 512 cm³

To Find -

Length of the Box

From above question, it is cleared that :-

• Breadth = 2 × Height
• Breadth = 1/2 × Length

Now,

» 2 × Height = 1/2 × Length

» Height = 1/2 × 2 × Length

» Height = 1/4 × Length

• » Height = Length/4

As we know that :-

• Volume of cuboid = L × B × H

As Given -

• Volume = 512 cm³

» 512 cm³ = L × Length/2 × Length/4

» 512 cm³ = L³/8

» 512 × 8 cm³ = L³

» 4096 cm³ = L³

» L = ³√4096

• » L = 16 cm

Hence,

The Length is 16 cm

Breadth = Length/2 = 16/2 = 8 cm

Height = Breadth/2 = 8/2 = 4 cm