Fill in the blanks in each of the following so as to make the statement true:

Solution:

(i) $1 \mathrm{~m}^{3}=1 \mathrm{~m} \times 1 \mathrm{~m} \times 1 \mathrm{~m}$

$=100 \mathrm{~cm} \times 100 \mathrm{~cm} \times 100 \mathrm{~cm} \quad(\because 1 \mathrm{~m}=100 \mathrm{~cm})$

$=1000000 \mathrm{~cm}^{3}$

$=10^{6} \mathrm{~cm}^{3}$

(ii) $1 \mathrm{~L}=\frac{1}{1000} \mathrm{~m}^{3}$

$=\frac{1}{1000} 1 \mathrm{~m} \times 1 \mathrm{~m} \times 1 \mathrm{~m}$

$=\frac{1}{1000} \times 10 \mathrm{dm} \times 10 \mathrm{dm} \times 10 \mathrm{dm}$

$=1 \mathrm{dm}^{3}$

(iii) $1 \mathrm{~kL}=1000 \mathrm{~L}$

$=1 \mathrm{~m}^{3}\left(1000 \mathrm{~L}=1 \mathrm{~m}^{3}\right)$

(iv) Volume of a cube of side $8 \mathrm{~cm}=(\text { side })^{3}=8^{3}=512 \mathrm{~cm}^{3}$

(v) Lenght of the wooden cuboid $=10 \mathrm{~cm}$

Breadth $=8 \mathrm{~cm}$

Its volume $=4000 \mathrm{~cm}^{3}$

Suppose that the height of the cuboid is $h \mathrm{~cm} .$

Then, volume of the cuboid $=$ length $\times$ breadth $\times$ height

$\Rightarrow 4000=10 \times 8 \times h$

$\Rightarrow 4000=80 \times h$

$\Rightarrow h=\frac{4000}{80}=50 \mathrm{~cm}$

(vi) $1 \mathrm{cu} \mathrm{dm}=1 \mathrm{dm} \times 1 \mathrm{dm} \times 1 \mathrm{dm}$

$=100 \mathrm{~mm} \times 100 \mathrm{~mm} \times 100 \mathrm{~mm}$

$=1000000 \mathrm{~mm}^{3}$

$=10^{6} \mathrm{cu} \mathrm{mm}$

(vii) $1 \mathrm{cu} \mathrm{km}=1 \mathrm{~km} \times 1 \mathrm{~km} \times 1 \mathrm{~km}$

$=1000 \mathrm{~m} \times 1000 \mathrm{~m} \times 1000 \mathrm{~m}(\because 1 \mathrm{~km}=1000 \mathrm{~m})$

$=1000000000 \mathrm{~m}^{3}$

$=10^{9} \mathrm{cu} \mathrm{m}$

(viii) $1 \mathrm{~L}=\frac{1}{1000} \mathrm{~m}^{3}$

$=\frac{1}{1000} \times 1 \mathrm{~m} \times 1 \mathrm{~m} \times 1 \mathrm{~m}$

$=\frac{1}{1000} \times 100 \mathrm{~cm} \times 100 \mathrm{~cm} \times 100 \mathrm{~cm} \quad(\because 1 \mathrm{~m}=100 \mathrm{~cm})$

$=1000 \mathrm{~cm}^{3}$

$=10^{3} \mathrm{cu} \mathrm{cm}$

(ix) $1 \mathrm{~mL}=\frac{1}{1000} \times 1 \mathrm{~L}=\frac{1}{1000} \times \frac{1}{1000} \mathrm{~m}^{3}$

$=\frac{1}{1000} \times \frac{1}{1000} \times 1 \mathrm{~m} \times 1 \mathrm{~m} \times 1 \mathrm{~m}$

$=\frac{1}{1000} \times \frac{1}{1000} \times 100 \mathrm{~cm} \times 100 \mathrm{~cm} \times 100 \mathrm{~cm} \quad(\because 1 \mathrm{~m}=100 \mathrm{~cm})$

$=1 \mathrm{cu} \mathrm{cm}$

(x) $1 \mathrm{~kL}=1000 \mathrm{~L}=1000 \times \frac{1}{1000} \mathrm{~m}^{3}=1 \mathrm{~m}^{3}$

$=1 \mathrm{~m} \times 1 \mathrm{~m} \times 1 \mathrm{~m}$

$=10 \mathrm{dm} \times 10 \mathrm{dm} \times 10 \mathrm{dm} \quad(\because 1 \mathrm{~m}=10 \mathrm{dm})$

$=1000 \mathrm{cu} \mathrm{dm}$

$=1000 \times 10 \mathrm{~cm} \times 10 \mathrm{~cm} \times 10 \mathrm{~cm} \quad(\because 1 \mathrm{dm}=10 \mathrm{~cm})$

$=1000000 \mathrm{~cm}^{3}$

$=10^{6} \mathrm{cu} \mathrm{cm}$