Question

Three cube-shaped boxes are stacked one above the other

The volumes of two of the boxes are 1,331 cubic meters each, and the volume of the third box is 729 cubic meters
What is the height of the stacked boxes in meters?

Answer 1

Answer: The height of the stacked boxes is 31 meters.

Explanation:

Since, the Volume of a cube = (side)³

The volume of first box = 1331 cubic meters,

⇒ (side)³ = 1331

⇒
`\text{ side}=1331^{(1)/(3)}=11\text{ meters}`

Similarly, the side of second box = 11 meters ( Because, both boxes have the same volume )

Now, the volume of third box = 729 cubic meters

⇒ ⇒ (side)³ = 729

⇒
`\text{ side}=729^{(1)/(3)}=9\text{ meters}`

Thus, the height of the stacked boxes = Side of first box + side of second box + side of third box

= 11 + 11 + 9

= 31 meters.

Answer 2

The height of the three cube - shaped boxes may be determined by getting the cube roots of their volumes. For the first two boxes with volumes of 1,331 m³ each, their heights are 11 m each. For the third box, the height is the cube root of 729 m³ and that is 9 m. The total height of the boxes is 31 meters.