Question

Fill in the blanks
The volume of a cube of side 1 cm is equal to.....m³
The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ....(mm)²
A vehicle moving with a speed of 18 km h^–1 covers....m in 1 s
The relative density of lead is 11.3. Its density is ....g cm^–3 or . ...kg m^–3.

Answer 1

1 cm = 1/100 m
Volume of the cube = 1 cm³
But, 1 cm3 = 1 cm × 1 cm × 1 cm = (1/100)m x (1/100)m x (1/100)m
therefore, 1 cm³ = 10^–6 m³
Hence, the volume of a cube of side 1 cm is equal to 10^–6 m³.
The total surface area of a cylinder of radius r and height h is
S = 2πr (r + h). Given that, r = 2 cm = 2 × 1 cm = 2 × 10 mm = 20 mm
h = 10 cm = 10 × 10 mm = 100 mm = 15072 = 1.5 × 10⁴ mm²

Therefore, S=2 x 3.14 x 20 x (20+100)

Using the conversion,

1km/h = 5/18 m/s

18km/h = 18x5/18 = 5m/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.
Relative density of a substance is given by the relation,