Question

a farmer digs a well of 10 m diameter and 14m depth and build an embankment with the earth dug out fine find the width of embankment if its height is 44÷37

Answer 1

Answer:

12.9 m

Step-by-step explanation:

Find the radius:

Radius = Diameter ÷ 2

Radius = 10 ÷ 2 = 5 m

Find the volume of the earth dug:

Volume = πr²h

Volume = π(5)²(14) = 1100 m³

Define x:

Let the width of the embankment be x

Find the area of the embankment base:

Area of the embankment base = π(x + 5)² - π(5)²

Area of the embankment base = π(x²  + 25 + 10x - 25)

Area of the embankment base = π(x²  + 10x)

Find the width of the embankment:

Volume = 1100 m³

Height = 44/37 m

π(x²  + 10x)(44/37) = 1100

(x²  + 10x))(44/37)= 350

44x² + 440x -12950 = 0

22x²  + 220x - 6475 = 0

x = 12.9 or x = -22.9 (rejected, since width cannot be negative)

Answer: The width is 12.9 m