012 Review Problem - Lake for household water supply | Solid Geometry Review at MATHalino

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

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Daily water consumption of 60,000 households
$V_c = 25(60,000) = 1,500,000 ~ \text{gal.}$

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

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

Volume of 1 ft. depth of water in the reservoir
$V_r = A_b h$

$A_b = 1000 \times 43,560 = 43,560,000 ~ \text{ft.}^2$

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

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

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

Number of days
$N = \dfrac{V_r}{V_c}$

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

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

012 Review Problem - Lake for household water supply

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