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Surface Area And Volume of A Cuboid And Cube — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsSurface Area And Volume of A Cuboid And Cube1 Mark
Question
A cube whose volume is $\frac18$ cubic centimeter is placed on a cube whose volume is 1cm3. The two cubes are then placed on top a third cube whose volume is 8cm3. The heigght of the stacked cubes is:
  1. 3.5cm
  2. 3cm
  3. 7cm
  4. None of these.
✓

Answer

  1. 3.5cm

​​​​​​​Solution:

Let,

V1, V2, V3 → Volume of the three cubes

a1, a2, a3 → Side of the three cubes

We know that,

a3 = V

So,

$\text{a}^3_1=\text{V}$

$\text{a}^3_1=\frac18$

$\text{a}_1=\frac12\text{cm}$

Similarly,

$\text{a}^3_2=1$

$\text{a}_2=1\text{cm}$

And;

$\text{a}^3_3=8$

$\text{a}_2=2\text{cm}$

So the height of the resulting structure,

$=\frac12+1+2$

= 0.5 +1 + 2

= 3.5cm

The height of the structure is 3.5cm.

Hence, the correct choice is (a).

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