A cube whose volume is 1 8 cubic centimeter is placed on top of a… - Vidyadip

MCQ

A cube whose volume is $\frac{1}{8}$ cubic centimeter is placed on top of a cube whose volume is $1\ cm^3$. The two cubes are then placed on top of a third cube whose volume is $8\ cm^3$. The height of the stacked cubes is:

A
None of these
B
$3\ cm$
✓
$3.5\ cm$
D
$7\ cm$

✓

Answer

Correct option: C.

$3.5\ cm$

Let $a, b, c.$ be the sides of three cubes
Then $a^3 =\frac{1}{8}\Rightarrow\text{a}=\frac{1}{2}$
$b^3= 1 ⇒ b = 1$
$c^3 = 8 ⇒ c = 2,$
Now height of resulting cube
$0.5 + 1 + 2 = 3.5\ cm$

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