Question

A cuboid is formed by joining two cubes of volume $216c{m}^3$. Total surface area of the cuboid will be .

• A. $180c{m}^2$
• B. $90c{m}^2$
• C. $200c{m}^2$
• D. $360c{m}^2$

Answer 1

The correct option is D $360c{m}^2$

Given: Volume of each cube
= $216c{m}^3$
A cuboid is formed by joining two such cubes.



Let a be the length of each side of the cube.
Volume of cube = $a^3$
$\Rightarrow$ $216c{m}^3$ = $a^3$
$\Rightarrow$ $a=6cm$

Now, length of the cuboid, l
= 2a = 2 $\times$ 6 = 12 cm
Breadth of the cuboid, b = a = 6 cm
Height of the cuboid, h = a = 6 cm

Total surface area of the cuboid
= 2(lb + bh + hl)
= $2(12\times 6+6\times 6+6\times 12)$
= $2(72+36+72)$
= $360c{m}^2$

$\therefore$ Total surface area of the cuboid is $360c{m}^2$.