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