__Question 2.1__:

Fill in the blanks

(a) The volume of a cube of side 1 cm is equal to .....m

^{3}

(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ...(mm)

^{2}

(c) A vehicle moving with a speed of 18 km h–

^{-1}covers....m in 1 s

(d) The relative density of lead is 11.3. Its density is ....g cm–

^{-3}or ....kg m–

^{-3}

^{}

__Solution__:

(a) 1 cm = 1 / 100 m

Volume of the cube = 1 cm

^{3}

But, 1 cm

^{3}= 1 cm × 1 cm × 1 cm = (1/100) m X (1/100) m X (1/100) m

∴1 cm

^{3}= 10

^{–6}m

^{3}

Hence, the volume of a cube of side 1 cm is equal to 10

^{–6}m

^{3}.

(b) The total surface area of a cylinder of radius

*r*and height

*h*is

*S*= 2π

*r*(

*r*+

*h*).

Given that,

*r*= 2 cm = 2 × 1 cm = 2 × 10 mm = 20 mm

*h*= 10 cm = 10 × 10 mm = 100 mm

∴ S = 2 X 3.14 X 20 X (20 + 100) = 15072 = 1.5 X 10

^{4}mm

^{2}

^{}(c) Using the conversion,

1 km/h = (5/18) m/s

18 km/h = 18 X (5/18) = 5 m/s

Therefore, distance can be obtained using the relation:

Distance = Speed × Time = 5 × 1 = 5 m

Hence, the vehicle covers 5 m in 1 s.

(d) Relative density of a substance is given by the relation,

Relative density = Density of substance / Density of water

= 11.3 X 1 = 11.3 g/cm

^{3}

Again, 1g = 1/1000 kg

1 cm

^{3}= 10

^{–6}m

^{3}

1 g/cm

^{3}= 10

^{-3}/ 10

^{-6}kg m

^{-3}= 10

^{3 }kg m

^{-3}

∴ 11.3 g/cm

^{3}= 11.3 × 10

^{3}kg/m

^{3}

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