Question

The rain water from a flat roof 5 m by 7 m drains into a tank which has dimensions 42 cm, 20 cm and 50 m. What depth of rainfall will fill the tank?

Answer 1

Given:

Roof dimensions = 5 m by 7 m.

Tank dimensions = 42 cm, 20 cm and 50 m (as written).

Let h = depth of rainfall (in metres) required to fill the tank.

Step-wise calculation:

Case A: If the tank dimensions are 42 cm, 20 cm and 50 cm:

1. Convert tank dimensions to metres: 

42 cm = 0.42 m

20 cm = 0.20 m

50 cm = 0.50 m

2. Tank volume

= 0.42 × 0.20 × 0.50 

= 0.042 m³

3. Roof area

= 5 × 7 

= 35 m²

4. Rainfall depth

h = `"Tank volume"/"Roof area"` 

= `0.042/35`

= 0.0012 m

= 0.12 cm

= 1.2 mm

Case B: If the tank dimensions are 42 cm, 20 cm and 50 m (literal):

1. Convert to metres:

42 cm = 0.42 m

20 cm = 0.20 m

50 m = 50 m

2. Tank volume

= 0.42 × 0.20 × 50

= 4.2 m³

3. Roof area = 35 m² (same).

4. Rainfall depth

h = `4.2/35`

= 0.12 m 

= 12 cm

= 120 mm

If the third tank dimension is 50 cm (most likely), the rainfall depth required is 0.0012 m = 1.2 mm.

If the third dimension is really 50 m (as written), the rainfall depth required is 0.12 m = 12 cm (120 mm).