Rainwater tank for a hill school
A school in Dhading plans a rainwater tank. The tank has a cylindrical body of radius 1.4 m and height 3 m, with a hemispherical dome on top. It sits on a flat concrete base on the ground. The outside, except the base, will be painted at NPR 250 per square metre. The inside, including the base, will be waterproofed at NPR 180 per square metre. The school roof has an area of 120 m² and receives 1,200 mm of rain in a year; about 80% can be collected. The school uses 600 litres per day. The principal wants to know the tank capacity, the two painting costs, and whether a year's rainfall can cover 200 school days without buying water. Use pi = 3.14.
1. Find the capacity of the tank in litres.
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The tank is a cylinder plus a hemisphere:
V = pi r²h + (2/3) pi r³.
With r = 1.4 m, h = 3 m, pi = 3.14:
- Cylinder = 3.14 × 1.96 × 3 = 18.4632 m³.
- Dome = (2/3) × 3.14 × 2.744 = 5.7441 m³.
- Total = 24.2073 m³.
Since 1 m³ = 1,000 litres, capacity ≈ 24,207 litres, or about 24.2 kL.
2. Calculate the outside painting cost and the inside waterproofing cost.
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Outside area excludes the base:
- Cylinder side = 2 × 3.14 × 1.4 × 3 = 26.376 m².
- Dome = 2 × 3.14 × 1.96 = 12.3088 m².
- Total outside = 38.6848 m².
- Painting cost = 38.6848 × 250 = NPR 9,671.20.
Inside area includes the base:
- Base = 3.14 × 1.96 = 6.1544 m².
- Side = 26.376 m².
- Dome = 12.3088 m².
- Total inside = 44.8392 m².
- Waterproofing cost = 44.8392 × 180 = NPR 8,071.06.
Combined cost ≈ NPR 17,742.26.
3. Can a year's rainfall cover 200 school days? Support your answer with calculations.
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Annual harvest = roof area × rainfall × collection efficiency
= 120 m² × 1.2 m × 0.80 = 115.2 m³ = 115,200 litres.
At 600 litres per day, this lasts 115,200 ÷ 600 = 192 school days.
For 200 days the school needs 200 × 600 = 120,000 litres. The harvest is short by 120,000 − 115,200 = 4,800 litres, about 8 days of use.
The tank itself holds 24,207 litres, only about 40 days of use without rain. So a year's rainfall cannot cover 200 school days; the school needs an extra 4,800 litres or must reduce use.