Question

1) In class you worked with a "big" cube made of 27 smaller cubes each of which was 1 cmby 1 cm by 1 cm. Suppose you had 150 of the small cubes, what is the largest "big" cubeyou could make? How do you know?

Answer 1

The information provided is that you have smaller cubes that measure 1 cm on either of the three sides. In order words if you lie each cube side by side you would have the length/width/height of the indicate sides.

For a cube made up of 27 smaller cubes, you can determine the length of each side by factoring the entire size provided. That means for a cube made up of 27 smaller cubes you would have;

$27=3\times3\times3$

This means you would have 3 smaller cubes on the length, 3 smaller cubes on the width and 3 smaller cubes on the height.

Therefore, if you now have 150 of the smaller cubes, by factoring this you would have the following possibility;

$\begin{gathered} 150=2\times3\times5\times5 \\ 150=6\times5\times5 \end{gathered}$

This means you would have one side (length) 6 cubes, on another side (width) 5 cubes and on the third side (height) 5 cubes.

That means with 150 smaller cubes you could make a cube with the dimensions,

$\begin{gathered} \text{Length}=6\operatorname{cm} \\ \text{Width}=5\operatorname{cm} \\ \text{Height}=5\operatorname{cm} \end{gathered}$

ANSWER:

The largest big cube you could make would be a 6 cm by 5 cm by 5cm big cube