Question

The length of the diagonal of a cube is 8 root 3cm.Find its: edge, total surface area, volume

Answer 1

V=root3*d^3/9
   =(root3)^4 8^3/9
   =9*512/9
   =512 cu cm
edge=cube root (V)
        =cube root 512
        =8cm
surface area=8*8*6
                    =384 sq cm

Answer 2

Answer:

The edge of the cube is 8 cm , total surface area of cube is    $384 cm ^2$  and volume of cube is   $512 cm^3$

Step-by-step explanation:

Formula of diagonal of cube = $\sqrt{3} a$

Where a is the side of the cube

Since we are given that The length of the diagonal of a cube is 8 root 3cm

So,  $8\sqrt{3}=\sqrt{3} a$

$8= a$

Thus the length of the side is 8 cm.

Total surface area of cube =$6a^{2}$

Where a is the length of the side

So, Total surface area of cube =$6(8)^{2}$

                                                   =$384 cm ^2$

Volume of cube = $a^{3}$

So, volume of given cube = $(8)^{3}$

                                           = $512 cm^3$

Hence the edge of the cube is 8 cm , total surface area of cube is    $384 cm ^2$  and volume of cube is   $512 cm^3$