Question

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 1

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 infer

a3=12a

⟹a3−12a=0⟹a(a2−12)=0

Therefore

a=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 .