Question

Fill in the blanks 

1. The volume of a cube of side 1 cm is equal to________\(m^3\).
2. The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to__________\(\text(mm)^2\).
3. A vehicle moving with a speed of 18 km \(h^{-1}\) covers ________m in 1 s.
4. The relative density of lead is 11.3. Its density is ....g \(\text {cm}^{-3}\) or ________kg \(\text m^{-3}\).

Answer 1

(a) Volume of a cube of side 1 cm

Side = 1 cm = 1 × 10⁻² m

Volume = (side)³

= (1 × 10⁻²)³ m³

= 1 × 10⁻⁶ m³

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(b) Surface area of a solid cylinder

Radius r = 2.0 cm, height h = 10.0 cm

Total surface area of a cylinder:

= 2πr(h + r)

= 2π × 2 × (10 + 2)

= 48π cm²

Convert cm² to mm²:
1 cm² = 100 mm²

Surface area = 48π × 100

= 4800π mm² ≈ 1.51 × 10⁴ mm²

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(c) Distance covered in 1 s

Speed = 18 km h⁻¹

Convert to m s⁻¹:

18 km h⁻¹ = 18 × (1000 / 3600)

= 5 m s⁻¹

Distance covered in 1 s = 5 m

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(d) Density of lead

Relative density of lead = 11.3

Density of water = 1 g cm⁻³

Density of lead = 11.3 × 1

= 11.3 g cm⁻³

Convert to kg m⁻³:
1 g cm⁻³ = 1000 kg m⁻³

Density of lead = 11.3 × 1000

= 1.13 × 10⁴ kg m⁻³

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Final Filled Blanks:

• (a) 1 × 10⁻⁶ m³
• (b) 4800π mm² (≈ 1.51 × 10⁴ mm²)
• (c) 5 m
• (d) 11.3 g cm⁻³ or 1.13 × 10⁴ kg m⁻³