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The volume of a cube is 343cm3343cm3. Then, the surface is ____.

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Detailed Solution

We know that a cuboid is a three dimensional object with six rectangular faces joined by 8 vertices. It has three different types of sides called length, breadth and height denoted

l, b

and

h

.
A cube is cuboid with 6 square faces with all sides of equal length. It means

l = b = h = a

volume of a cuboid is

l × b × h

. So we calculate the volume of a cube with denoting as

V

V = l × b × h = a × a × a = a 3

The surface area of the cube is the sum of areas of 6 square faces. The area of 1 square face is

a × a = a 2

TSA = 6 a 2

We are given the question that the volume of a cube is

343 c m 2

. Let us denote its volume as

V

and length of the side as

a

. So we have

V = 343 c m 3 ⇒ a 3 = 343 c m 3

a = (343 c m 3) 13 = ((7 c m) 3) 13 = 7 c m

TSA = 6 a 2 TSA = 6 × (7) 2 TSA= 294 c m 2

Hence, the Surface is

294 c m 2

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