# 012 Review Problem - Lake for household water supply

**Problem 12**

The water supply of a district consists of a lake whose surface area is 1000 acres. The number of household supplied with water is 60,000. Supposing each household to use 25 gal. per day, calculate how many days’ supply (to the nearest day below the exact number) is represented by a depth of 1 ft. of water in the lake. (1 acre equals 43,560 sq. ft.)

**Solution 12**

Daily water consumption of 60,000 households

$V_c = 25(60,000) = 1,500,000 ~ \text{gal.}$$A_b = 1000 \times 43,560 = 43,560,000 ~ \text{ft.}^2$

$V_c = 25(60,000) = 1,500,000 ~ \text{gal.}$

$V_c = 1,500,000 ~ \text{gal.} \times \dfrac{1 ~ \text{ft.}^3}{7.48 ~ \text{gal.}}$

$V_c = 200,535 ~ \text{ft.}^3$

Volume of 1 ft. depth of water in the reservoir

$V_r = A_b h$

$h = 1 ~ \text{ft.}$

$V_r = 43,560,000(1)$

$V_r = 43,560,000 ~ \text{ft.}^3$

Number of days

$N = \dfrac{V_r}{V_c}$

$N = \dfrac{43,560,000}{200,535}$

$N = 217 ~ \text{days}$ *answer*

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