Question

(Exponents)

You have 1,000,000 number cubes, each measuring one inch on a side.


If you stacked the cubes on top of one another to make an enormous tower, how high would they reach? Explain your reasoning.

If you arranged the cubes on the floor to make a square, would the square fit in your classroom? What would its dimensions be? Explain your reasoning

Answer 1

Part a) You have 1,000,000 number cubes, each measuring one inch on a side. If you stacked the cubes on top of one another to make an enormous tower, how high would they reach?

we know that

The high of one cube is equal to 1 in

so

to find the high of 1,000,000 cubes

Multiply the high of one cube by 1,000,000

so

`1*1,000,000=1,000,000 in=1*10^(6) in`

therefore

the answer part a) is

`10^(6) in`

Part b) If you arranged the cubes on the floor to make a square, would the square fit in your classroom? What would its dimensions be?

we know that

the area of a square is equal to

`A=b^(2)`

where

b is the length side of the square

so

`1,000,000=b^(2)\\b=√(1,000,000) \\b=1,000\ in`

the dimensions of the square would be 1,000 in x 1,000 in

convert to cm

we know that

1 in is-------> 2.54 cm

so

1,000 in=1,000*2.54=2,540 cm------> 25.40 meters

the dimensions of the square in meters would be 25.40 m x 25.40 m

It is possible that the square will fit in the classroom.