A pool has a volume of 3,105ft^3. Read details for more. Geometry homework. Please help!

Question

height of the water in deep end is 4x shallow end. deep end has 6 2/3 amount of water as shallow end. Find length d and height h of water in deep end. height of water in shallow end is 10ft, and length of water in shallow end is 9ft.

apologize for broken English (:

Answer 1

Let's start with volume of water (V = V of shallow + V of deep = V1 + V2)

V = 3105 = V1 + 6.67 V1 = 7.67 V1 ----> V1 = 405 ft3

V1 = d1 . w1. h1 or 405 = 9 x 10 x w ----> w = 4.5 ft (width of pool)

Width of pool is the same for both shallow and deep parts of the pool, therefore:

V2 = 6.67 V1 = 2701 ft3 = d2. w2. h2 = d2 . (4.5). (4 x 10) = 180 d2

Therefore d2 = 2701/180 = 15 ft (length of deep part)

And of course height is 4 times the shallow part or 40 ft.

Hope you can follow the math.