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The surface area of a cube is numerically equal to the total length of all its edges. Find its volume in cubic units.1) 2 cu. units 2) 6 cu. units 3) 8 cu. units 4) 5 cu. units 5) 7 cu. units |
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Answer» A CUBE has 6 square FACES. If the length of the edge of a cube is a, then area of one FACE is A2. So, total surface area lf the cube is equal to the sum of areas of all 6 square faces.Total Surface Area Of Cube=6a2 The problem states that the volume of the cube is equal to the sum of lengths of all edges.A cube has 12 edges.Volume of Cube=a3 Since length of an edge is assumed to be ‘a' units, from the problem statement we can infera3=12a ⟹a3−12a=0⟹a(a2−12)=0 Thereforea=0 or a2−12=0 Now, a = 0 is not possible because zero-length edge can't form a cube.Thus,a2=12 Now Total Surface Area=6a2 Substitute a2=12 in the above formula:Area=6×12=72 sq. units . |
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