Question

Laney builds a tower with wooden cubes. The bottom cube's edges are 8 centimeters long. The middle cube's edges are 2 centimeters shorter than the bottom cube. The top cube's edges are 2 centimeters shorter than the middle cube. What is the total volume of the cubes in the tower?

Answer 1

Answer: The total volume of the the cubes in the tower is 792 cubic centimetres (792 cm³)

Step-by-step explanation: We shall call the volume of the cube at the bottom VB, the volume of the cube at the middle VM, and the volume of the cube at the top VT. The tower is made up of cubes at different levels and at the bottom the cube measures 8 centimetres. The cube at the middle measures 2 cm less than the bottom cube, hence middle cube equals 8 minus 2 which equals 6 cm. The top cube measures 2 cm less than the middle cube, hence the top cube equals 6 minus 2 which equals 4 cm. The volume of each cube is given as;

Volume = L³

The length of a cube measures the same on all sides, that is, length, width and height. The length on all sides therefore of the bottom cube is 8 cm. The volume equals;

VB = 8³

VB = 512 cm³

The length on all sides of the middle cube is 6 cm (measures 2 cm shorter than the bottom cube). The volume of the middle cube equals;

VM = L³

VM = 6³

VM = 216 cm³

The length on all sides of the top cube is 4 cm (measures 2 cm shorter than the middle cube). The volume of the top cube equals;

VT = L³

VT = 4³

VT = 64

From the calculations shown, the total volume of the cubes in the tower is given as;

Total volume = VB + VM + VT

Total volume = 512 + 216 + 64

Total volume = 792 cm³

Total volume is 792 cubic centimetres.

Answer 2

Answer: The total volume of the cubes is 792 cm^3

Explanation:

We have 3 cubes here.

And remember that the volume of a cube is equal to the length of one of the edges at the power of 3.

So for the bottom cube, we have that the edges are 8cm long, so the volume of this cube is:

V1 = 8cm^3 = 512cm^3

The edges of the next cube are 2cm shorter, so the edges are 6cm long.

Then the volume is:

V2 = 6cm^2 = 216cm^3

The top cube's edges are 2 cm shorter than the previous one, so the length of these edges is 4cm, then the volume is:

V3 = 4cm^3 = 64cm^3

Now, the total volume is equal to:

V = V1 + V2 + V3 = 512cm^3 + 216cm^3 + 64cm^3 = 792 cm^3