Question

Need help ASAP

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?
A.
19
B.
29
C.
30
D.
31

Answer 1

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

⇒

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

⇒

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

31

Explanation:

The volume of a cube is define as l x l x l= l(3) [l cubed]

So in the first case the volume =1331

From l x l x l= 1331; l= the cube root of (1331) = 11m;

So the total volume of the compactment is the sum of the 3 stacks= 1331 + 1331 + 729 = 2391 m3

Remember that volume is the same as base area X height

Let's denote this as V= B X h

Now h= V/ B

Remember that the first box placed at the base has a volume of 1331m3

That volume was a result of l x l x l= base area x height; the base area in this case= l x l ; since the surface facing the ground is a square.

With that in mind

The base area of the first cube= 11 X 11= 121

This area is the same as that of the whole stack;

Hence our formula H= V/ B can be used

h = 2391/121 =19.76m

Alternatively since this box is a solid box we take a look at the height of each box

Adding all 3 gives the height of the stack

The first two boxes are the same and the height is 11

Combining them we have 22m

The 3rd box height = the cube root of the volume of the third box = 9 [9x9x9=729]

Hence the total height of the compactment is

11+11+9=31m

31 is the most correct ; if it were a liquid volume that had to do with mixture ; the first answer would have been the most probable solution.