Question

If the diagonal of a cube is $16\sqrt{3}$ cm., then its surface area and volume are respectively

• A. $1456{cm}^2$ and $4096{cm}^3$
• B. $1626{cm}^2$ and $1024{cm}^3$
• C. $1226{cm}^2$ and $1024{cm}^3$
• D. $1536{cm}^2$ and $4096{cm}^3$

Answer 1

Answer: (D)

$1536{cm}^2$ and $4096{cm}^3$

Length of the diagonal of a cube $=\sqrt{3}\times$ side $=16\sqrt{3}$
Thus, length of the side of the cube, $a=16$ cm
Now, total surface area of the cube of edge $=6a^2$

So, the surface area of this cube $=1536$ sq.cm

Volume of a cube of edge $=a^3$

$\therefore V={16}^3=4096{cm}^3$

Hence, option D is the correct answer.