Question

The width of a box is two-third of it's length and height is one-third of it's length. If the volume of the box is 384 cubic meter, find the dimensions of the box.​

Answer 1

Length - 12 m, width - 8m, height - 4 m

--------------------------------------

The relation between dimensions of the box:

• w = (2/3)l;
• h = (1/3)l;
• V = 384 m³.

Use volume equation and find the value of l:

• V = lwh

• 384 = l*(2/3)l*(1/3)l
• 384 = 2/9l³
• l³ = 384*9/2
• l³ = 1728
• l = ∛1728
• l = 12 m

Find the width and height:

• w = (2/3)*12 = 8 m
• h = (1/3)*12 = 4 m