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

Maharashtra BoardEnglish MediumSTD 9MathsSurface Area And Volume of A Cuboid And Cube1 Mark
MCQ
A cube whose volume is $\frac18$ cubic centimeter is placed on a cube whose volume is $1cm^3$. The two cubes are then placed on top a third cube whose volume is $8cm^3$. The heigght of the stacked cubes is:
​​​​​​​​​​​​​​
  • ✓
    $3.5cm$
     
  • B
    $3cm$
     
  • C
    $7cm$
     
  • D
    None of these.
✓

Answer

Correct option: A.
$3.5cm$
 
$3.5cm$​​​​​​​
Let,
$V_1, V_2, V_3$ → Volume of the three cubes
$a_1, a_2, a_3$ → Side of the three cubes
We know that,
$a^3 = V$
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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