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If the sum of the lengths of all the edges of a cube is 228 centimeters, find its volume.
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Letโs begin by recalling how to find the volume of a cube.
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The volume is equal to ๐ multiplied by ๐ multiplied by ๐, or ๐ cubed, where ๐ represents the edge length of the cube.
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We havenโt been told the edge length of this cube directly, instead weโve been told that the sum of the lengths of all the edges is 228 centimeters.
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In order to calculate what the length of one edge is, we need to consider how many edges a cube has.
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There are four edges on the front face of the cube.
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There are another four edges on the back face of the cube.
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There four more edges connecting these two faces together, making a total of 12 edges overall.
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Now that we know that the cube has 12 edges and theyโre all of equal length, we can express this as an equation.
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As the sum of the lengths of all the edges is 228 centimeters, we have the equation 12๐ is equal to 228.
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To solve this equation, we need to divide both sides by 12, giving ๐ is equal to 19.
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Therefore the edge length of the cube is 19 centimeters.
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Now letโs find its volume.
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The volume of the cube is equal to its edge length cubed, 19 cubed, which is 6859.
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The units for volume are cubic units, so we have that the volume of this cube is 6859 cubic centimeters.