Fill in the blanks in each of the following so as to make the statement true:
(i) 1 m³ = .........cm³
(ii) 1 litre = ....... cubic decimetre
(iii) 1 kl = ....... m³
(iv) The volume of a cube of side 8 cm is ........
(v) The volume of a wooden cuboid of length 10 cm and breadth 8 cm is 4000 cm³. The height of the cuboid is ........ cm.
(vi) 1 cu.dm = ........ cu. mm
(vii) 1 cu. km = ........ cu. m
(viii) 1 litre = ........ cu. cm
(ix) 1 ml = ........ cu. cm
(x) 1 kl = ........ cu. dm = ........ cu. cm.

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Solution

$(i) 1 m^{3} = 1 m \times 1 m \times 1 m = 100 cm \times 100 cm \times 100 cm (∵ 1 m = 100 cm) = 1000000 {cm}^{3} = 10^{6} {cm}^{3} (ii) 1 L = \frac{1}{1000} m^{3} = \frac{1}{1000} 1 m \times 1 m \times 1 m = \frac{1}{1000} \times 10 dm \times 10 dm \times 10 dm = 1 {dm}^{3} (iii) 1 kL = 1000 L = 1 m^{3} (1000 L = 1 m^{3}) (iv) Volume of a cube of side 8 cm = (side)^{3} = 8^{3} = 512 {cm}^{3} (v) Lenght of the wooden cuboid = 10 cm Breadth = 8 cm Its volume = 4000 {cm}^{3} Suppose that the height of the cuboid is h cm . Then, volume of the cuboid = length \times breadth \times height \Rightarrow 4000 = 10 \times 8 \times h \Rightarrow 4000 = 80 \times h \Rightarrow h = \frac{4000}{80} = 50 cm (vi) 1 cu dm = 1 dm \times 1 dm \times 1 dm = 100 mm \times 100 mm \times 100 mm = 1000000 {mm}^{3} = 10^{6} cu mm (vii) 1 cu km = 1 km \times 1 km \times 1 km = 1000 m \times 1000 m \times 1000 m (∵ 1 km = 1000 m) = 1000000000 m^{3} = 10^{9} cu m (viii) 1 L = \frac{1}{1000} m^{3} = \frac{1}{1000} \times 1 m \times 1 m \times 1 m = \frac{1}{1000} \times 100 cm \times 100 cm \times 100 cm (∵ 1 m = 100 cm) = 1000 {cm}^{3} = 10^{3} cu cm (ix) 1 mL = \frac{1}{1000} \times 1 L = \frac{1}{1000} \times \frac{1}{1000} m^{3} = \frac{1}{1000} \times \frac{1}{1000} \times 1 m \times 1 m \times 1 m = \frac{1}{1000} \times \frac{1}{1000} \times 100 cm \times 100 cm \times 100 cm (∵ 1 m = 100 cm) = 1 cu cm (x) 1 kL = 1000 L = 1000 \times \frac{1}{1000} m^{3} = 1 m^{3} = 1 m \times 1 m \times 1 m = 10 dm \times 10 dm \times 10 dm (∵ 1 m = 10 dm) = 1000 cu dm = 1000 \times 10 cm \times 10 cm \times 10 cm (∵ 1 dm = 10 cm) = 1000000 {cm}^{3} = 10^{6} cu cm$

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Fill in the blanks in each of the following so as to make the statement true:
(i) 1 $m^{3}$ = ___ $c m^{3}$
(ii) 1 litre = ___ cubic decimetre
(iii) 1 kl = ___ $m^{3}$
(iv) The volume of a cube of side 8 cm is ___.
(v) The volume of wooden cubiod of length cm and breadth 8 cm = is 4000 $c m^{3}$ . The height the cubiod is ___ cm
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(vii) 1 cu km = ___ cu.m
(viii) 1 litre = ___ cu.cm
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