Question

The volume of a cuboid is twice the volume of a cube If the dimensions of the cuboid are 9 cm 8 cm and 6 cm the total surface area of the cube is :

• A. $72c{m}^2$
• B. $216c{m}^2$
• C. $432c{m}^2$
• D. $108c{m}^2$

Answer 1

Answer: (B)

$216c{m}^2$

Here length of cuboid $=9cm$, breadth of cuboid $=8cm$ and height of cuboid $=6cm$
$\therefore$ volume of cuboid $=$ length $\times$ breadth $\times$ height
$=9cm\times 8cm\times 6cm=432c{m}^3$ .
According to question:
volume of cuboid = $2\times$ volume of cube
$432c{m}^3=2\times (side{)}^3$
$\Rightarrow 216c{m}^3=(side{)}^3$
$\Rightarrow (6cm{)}^3=(side{)}^3$
$\therefore$ Side of cube = 6 cm.
Since, total surface area of the cube = $6\times sid{e}^2$
=$6\times (6cm{)}^2=216c{m}^2$