Video Transcript
If the perimeter of the base of a
cube is 54.4 centimeters, find its total surface area.
The base of a cube is a square. Here’s the base, and the perimeter
of this square is 54.4 centimeters. The distance around the base
measures this much. We know that the base of a cube is
a square and that in a square all sides are equal. If we add up all four of the sides,
side plus side plus side plus side, it would be 54.4 centimeters.
In order to solve the problem
though, we need to find out how much one side is worth. We have to divide 54.4 by four. How many times does four go into
five? One time. One times four equals four. Five minus four equals one. Bring down the next digit. How many times does four go into
14? Three times. Three times four equals 12. 14 minus 12 equals two. Make sure we line up our decimal
point for the quotient, and then bring down the next digit.
How many times can four go into
24? Six times. Six times four equals 24. 24 minus 24 equal zero. There is no remainder. This tells us that each of our
sides measure 13.6 centimeters. We’ve only found the length of one
side, but what is our goal here? Our goal is to find the total
surface area of a cube. We know that the surface area of a
cube is the area of all six faces added together. Let’s start by finding the area of
the base.
Remember that the base is a square,
and we know a side length. And to find the area of a square,
we square its side length. Multiply side by side. We need to square 13.6. To do that, we multiply 13.6 times
13.6. Six times six is 36. Six times three is 18, plus the
three we carried over equals 21. Write down the one; carry the
two. Six times one is six, plus the two
we carried over equals eight.
Now we’ll start multiplying with
the three. Three times six equals 18. Write down your eight; carry your
one. Three times three equals nine, plus
one equals 10. Write down the zero; carry the
one. Three times three is three, plus
one is four. Now we’re multiplying by one. One times six equals six. One times three equals three. One times one equals one. From there, we add all the partial
products.
Bring down the six. One plus eight equals nine. Eight plus zero plus six equals
14. Write down the four; carry the
one. One plus four plus three equals
eight. And then we bring down the one. We’re dealing with two decimal
places. So we put our decimal two places to
the left. And we’ve found the area of the
base: 184.96 centimeters squared. Now that we know the area of one of
the sides, we can find the total surface area.
A cube has six identical faces, and
that means we can take the area of one of the faces and multiply it by six. To find the total surface area,
184.96 times six will give us our total surface area. Six times six equals 36. Six times nine is 54, plus three is
57. Six times four is 24, plus five is
29. Six times eight is 48, plus two is
50. Six times one is six, plus five is
11.
We see that there are two decimal
places in our problem, and there will be two decimal places in the solution. By multiplying the area of one of
the faces by six, we’ve found the total surface area to be 1109.76 centimeters
squared.
