Question

What will be the volume of cube of side 0.01m in $\text{c}{{\text{m}}^{3}}$? \[\]
A.0.01\[\]
B.1\[\]
C.0.0001\[\]
D.0.000001\[\]

Answer 1

Hint: We recall the definition cuboid and cube. We use the formula for volume $V$ of a cube as $V={{\text{a}}^{3}}$. We find the volume of a cube with length of the side 1cm in $\text{c}{{\text{m}}^{\text{3}}}$and with length of the side 1m in $\text{c}{{\text{m}}^{3}}$by using the metric conversion 1m=100cm. We find the volume of the given cube side length 0.01m in ${{\text{m}}^{3}}$ and then convert it to $\text{c}{{\text{m}}^{\text{3}}}$.\[\]

Complete step by step answer:

 We know that a cuboid is a three dimensional object with six rectangular faces joined by 8 vertices. It has three different types of sides called length, breadth and height denoted $l,$$b$ and $h$. \[\]
A cube is cuboid with 6 square faces with all sides of equal length. It means $l=b=h=a$ (we denote).
The amount of space contained by a three dimensional object is measured by the quantity called volume. The amount of space that is occupied by a cuboid is the product of length, breadth and height. Mathematically, the volume of a cuboid is $l\times b\times h$. So we calculate the volume of a cube with denoting as $V$.
\[V=l\times b\times h=a\times a\times a={{a}^{3}}\]
So the amount of space contained in a cube of side 1cm is ${{V}_{\text{cm}}}=1\text{cm}\times 1\text{cm}\times 1\text{cm}=1\text{c}{{\text{m}}^{3}}$ of space. So now we find the volume of a cube with a side 1metre (m).
\[{{V}_{\text{m}}}=1\text{m}\times 1\text{m}\times 1\text{m}=100\text{cm}\times 100\text{cm}\times 100\text{cm}=100000c{{m}^{3}}\]
We are given the question that the length of the side of the cube is 0.01m. So its volume will be
\[V=0.01\text{m}\times 0.01\text{m}\times 0.01\text{m}=0.000001{{\text{m}}^{3}}\]
We convert the volume into $\text{c}{{\text{m}}^{3}}$ and have,
\[V=0.000001\times 100000\text{c}{{\text{m}}^{3}}=1\text{c}{{\text{m}}^{3}}\]

So, the correct answer is “Option B”.

Note: We can directly find the volume by converting the length of the side from metre to centimetre and then using the volume formula. The total surface area of the cube is given by $6{{a}^{2}}$ and the total surface area of the cuboid is given by $2\left( lb+bh+hl \right)$. The amount of liquid contained by a cube of side length 1cm is called 1 millilitre.