Question

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The volume of a cube is 1728cm^3.find its diagonal and tsa.

Answer 1

Let side of the cube be a.Its volume will be a³ which is equal to 1728.from this we get a=12.TSA will be 6a²=6*144=864
General formula for the diagonal of a cube if each side of the cube = s

Use Pythagorean Theorem to get the diagonal across the base:

s2 + s2 = h2

And again use Pythagorean Theorem to get cube’s diagonal, then solve for d:

h2 + s2 = d2

s2 + s2 + s2 = d2

3 * s2 = d2

d = √ (3 * s2) = s √3

So, if s = 3 then the answer is 3√3

Answer 2

but the question is of only 5 points. ..
So, I will present only 1/5 the solution

Volume of Cube = side^3

Side^3 = 1728
Side = 12

TSA of Cube = 6side^2
Diagonal of Cube = √3a

now u can easily find using the formulas given above