Download How do I calculate the side of a square or cube when

How do I calculate the length of the edge of a square or cube when given only the area or volume?
In your previous lessons you learned how to calculate the area of a square. Let’s review the concept
of area. When measuring the length of a line, you use another line to measure (a ruler). When you
measure the area of a 2 dimensional object, you use another two-dimensional object to measure
(mathematicians use squares to measure two dimensional objects, including circles!!) The area of
square is measured by how many smaller squares will fit inside of it. Let’s look at the big square
below and see if we can calculate the area:
The square is five by five units and we want to know how many square units (1 by 1 squares) will
fit inside. We could count each square unit one by one, but there is an easier way. We can multiply
the length of the large square times the width of the large square to get the area of the large square.
5*5 = 25 units2 or 25 square units. We could have also structured the equation like this 52=25
units2.
But what would we do if we were asked to find the length of a side of a square and all we knew was
the area of the square? Lets see another square below:
Well we know that whatever the length is times whatever the width is will equal the area of the
square. In other words we could write an equation that might look like this :
x * x = 9 units2.
If I multiply the same number together 2 times to get nine what would that number be? Could it be
2? No, because 2*2 = 4 and not nine. Is it 3? Yes, because 3*3=9! Now if 3 * 3 = 32, then x * x =
x2, so we could write the equation like this:
x2 = 9.
Think about this…
also equals to
which also equals to
which equals 3. Think about
this also…
is the same as
or, which = x. Just because we have letters under the radical
symbol does not mean that we do not treat them just like numbers!
So how can I solve an equation with an exponential expression in it quickly? I will show you how:
Now lets look at how to find volume of a cube.
When measuring the length of a line, you use another line to measure (a ruler). When you measure
the area of a 2 dimensional object, you use another two-dimensional object to measure
(mathematicians use squares to measure two dimensional objects, including circles!!). When you
measure the volume a three-dimensional object, you use another 3 dimensional object to measure
(mathematicians use cubes to measure three dimensional objects, including cylinders!). The volume
of a cube is measured by how many smaller cubes will fit inside of it. Let’s look at the cube below
and see if we can calculate the volume:
The cube is four by four by four units and we want to know how many cubic units (1 by 1 by 1
cubes) will fit inside. We could count each cubic unit one by one, but there is an easier way. We
can multiply the length times the width times the height of the cube to calculate the volume.
4*4 *4 = 64 units3 or 64 cubic units. We could have also structured the equation like this 43=64
units2.
But what would we do if we were asked to find the length of a side of a cube and all we knew was
the volume of the cube? Lets see another cube below:
Well we know that whatever the length times the width times the height is will equal the volume of
the cube. In other words we could write an equation that might look like this: x * x * x = 27 units3.
If I multiply the same number together 3 times to get 27 what would that number be? Could it be 2?
No, because 2*2*2 = 8 and not 27. Is it 3? Yes, because 3*3*3=27! Now if 3 * 3 * 3 = 33, then
x*x*x = x3, so we could write the equation like this:
x3 = 27.
Think about this…
also equals to
which also equals to
which equals 3. Think
about this also…
is the same as
which = x. Just because we have letters under the
radical symbol does not mean that we do not treat them just like numbers!
So how can I solve an equation with an exponential expression in it quickly? I will show you how:
We learned that after solving our equation that the length of each side is 3 whether it is the length,
width, or height…because it is a cube!
Get ready to try some practice!!!
Practice set. Solve the following problems. Write the equation first and then solve the problem. Be
sure to include the correct unit of measure in your answer.
1. Find the length of the edge of a square that has an area of 4 square inches
2. Find the length of the edge of a square that has an area of 81 square inches.
3. Find the length of the edge of a square that has an area of 49 square inches.
4. Find the length of the edge of a square that has an area of 64 square inches.
5. Find the length of the edge of a square that has an area of 121 square inches.
6. Find the length of the edge of a cube that has a volume of 1728 cubic inches.
7. Find the length of the edge of a cube that has a volume of 1331 cubic inches.
8. Find the length of the edge of a cube that has a volume of 512 cubic inches.
9. Find the length of the edge of a cube that has a volume of 216 cubic inches.
10. Find the length of the edge of a cube that has a volume of 343 cubic inches.