D. NUMERICALS - Solved Easy Way

Class 7 Physics - Physical Quantities and Measurement

1. Water Tank Volume

Given: Length = 5 m, Breadth = 2.5 m, Height = 1.25 m
Volume = Length × Breadth × Height
Volume = 5 × 2.5 × 1.25 = 15.625 m³
(a) In m³: 15.625 m³
(b) In litre: 15.625 × 1000 = 15,625 litre
Trick: 1 m³ = 1000 litre

2. Volume of Silver Piece

Given: Water rises from 50 mL to 62 mL
Volume of solid = Rise in water level
Volume = 62 - 50 = 12 mL = 12 cm³
Trick: 1 mL = 1 cm³

3. Volume of Liquid in Dish

Given: Dish = 10 cm × 10 cm × 5 cm
Volume = 10 × 10 × 5 = 500 cm³ = 500 mL

4. Area of Rectangular Field

Given: Length = 60 m, Breadth = 35 m
Area = Length × Breadth
Area = 60 × 35 = 2100 m²

5. Area of Irregular Lamina

Given: Graph paper, 1 square = 1 cm²
Count: Full squares + Half squares
Full squares ≈ 15, Half squares ≈ 12 = 6 full
Total area ≈ 15 + 6 = 21 cm²

6. Density of Brass

Given: Volume = 30 cm³, Mass = 252 g
Density = Mass ÷ Volume
(i) In g/cm³: 252 ÷ 30 = 8.4 g/cm³
(ii) In kg/m³: 8.4 × 1000 = 8400 kg/m³
Trick: 1 g/cm³ = 1000 kg/m³

7. Volume of Iron Ball

Given: Mass = 312 g, Density = 7.8 g/cm³
Volume = Mass ÷ Density
Volume = 312 ÷ 7.8 = 40 cm³

8. Mass of Cork

Given: Volume = 25 cm³, Density = 0.25 g/cm³
Mass = Density × Volume
Mass = 0.25 × 25 = 6.25 g

9. Density of Water

Given: Mass = 5 kg = 5000 g, Volume = 5 litre = 5000 cm³
Density = 5000 ÷ 5000 = 1 g/cm³

10. Cubical Tank

Given: Side = 1 m, Mass = 800 kg
(i) Volume = 1 × 1 × 1 = 1 m³
(ii) Density = 800 ÷ 1 = 800 kg/m³

11. Mass of Iron Block

Given: 2 m × 0.5 m × 0.25 m, Density = 7.8 g/cm³
Convert to cm: 200 × 50 × 25 = 250,000 cm³
Mass = 7.8 × 250,000 = 1,950,000 g = 1950 kg

12. Volume & Density of Lead

Given: Water rises 20 mL to 30 mL, Mass = 115 g
(i) Volume = 30 - 20 = 10 cm³
(ii) Density = 115 ÷ 10 = 11.5 g/cm³ = 11,500 kg/m³

13. Density of Copper

Given: 8.9 g/cm³
8.9 × 1000 = 8900 kg/m³

14. Speed of Car

Given: 15 km in 20 min
Speed = Distance ÷ Time
20 min = 1/3 h
(i) 15 ÷ (1/3) = 45 km/h
(ii) 45 × 5/18 = 12.5 m/s
Trick: km/h to m/s = × 5/18

15. Time Taken by Train

Given: 200 km, 60 km/h
Time = Distance ÷ Speed
Time = 200 ÷ 60 = 3.33 h = 3 h 20 min

16. Distance by Boy

Given: 10 m/s for 30 min
30 min = 1800 s
Distance = 10 × 1800 = 18,000 m = 18 km

17. Convert 36 km/h to m/s

36 × 5/18 = 10 m/s

18. Convert 15 m/s to km/h

15 × 18/5 = 54 km/h
Trick: m/s to km/h = × 18/5

CASE STUDY - Gunjan's Blocks

Given: Cube = 5×5×5 cm, Mass = 250 g
(i) Same size, different mass → Made of different materials
(ii) Volume = 125 cm³, Density = 250 ÷ 125 = 2 g/cm³
(iii) Property = Density
(iv) Double volume, same density → Mass = 500 g

Easy Memory Tricks

1. Density: How tightly "stuff" is packed. Heavy for size = high density
2. Units: 1 m³ = 1000 L, 1 L = 1000 cm³, 1 cm³ = 1 mL
3. Speed: km/h to m/s × 5/18, m/s to km/h × 18/5