Question

The length of the diagonal of a cube is 8 root 3 cm. Find its edge, TSA, Volume

Answer 1

Let the edge of the cube be a.

so, the diagonal √3a=8√3

=> a=8

Surface area = 6a²=6x8x8=384cm²
volume=a³=8³=512cm³

Answer 2

Answer:

i)Edge of the cube(a) = 8 cm

ii)Total surface area of the cube(TSA) = 384 cm²

iii)Volume of the cube (V) = 512 cm³

Step-by-step explanation:

Let edge of a cube = a cm

Diagonal (d) = 8√3 cm (given)

$We\: know\:that \:$

$\boxed { Diagonal \: of \: a \: cube\: (d) \\=\sqrt{3}a}$

$\implies \sqrt{3}a = 8\sqrt{3}$

$\implies a = \frac{8\sqrt{3}}{\sqrt{3}}$

After cancellation, we get

$\implies a = 8 \: cm$

Therefore,

i ) Edge of the cube(a) = 8 cm

ii ) Total surface area of the cube(TSA) = 6a²

= 6 × (8cm)²

= 6 × 64 cm²

= 384 cm²

iii ) Volume of the cube (V)

= a³

= (8 cm)³

= 512 cm³

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