Question

if the volume of cube is 729 cm3 what is the total length of its edges what is the total surface area

Answer 1

Let x = side of a cube                      Volume = 729 cm³

Volume = (x) (x) (x)     or  V = x³

 729 = x³

∛729 = ∛x

∛729 = x

     9 = x       Side a cube is 9 cm

To find surface area of a cube:

     Surface Area = 6x²

     Surface area = 6 (9)²

                             = 6 (81)

                              =  486 cm³

                             

Answer 2

let a be the edge of cube .

volume of the cube = 729 cm^3

Find the edge:
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since, we know that

volume of cube = ( edge)^3 = a^3

a^3 = 729 => a = cube√729

a = 9cm

edge of cube = 9cm

Find the total length:
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total length of edges = perimeter of cube

= 12a = 12 × 9 = 108 cm

Find the area:
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are of the cube = 6 ( edge )^2 = 6a^2

area of the cube = 6 (9)^2

6 × 81 = 486 cm^2

therefore,

total surface area of the cube

= 486cm^2

total length of edges = 108 cm

Answer: p = 108cm, area = 486cm^2
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