A well of diameter 2 m is dug 14 m deep. The earth taken out of it is

1.	A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to form and embankment of height 40 cm. Find the width of the embankment.
Answer» Let us assume shape of well is like a solid circular cylinder Radius of cylinder, r = 2/2 = 1m Depth(height) of well, h = 14m Volume of right circular cylinder, V’ = πr² h =\(π\times{1}^2\times14\)---------(I) Given that, length of embankment, l = 40 cm Let width of the embankment be x m Volume of the embankment, V’’ = π^r2 h = π ((1+x)² – 1)² x 0.4 -----------(II) Since well is spread evenly to form the embankment, so their volumes, V’ = V’’ ⇒ π × 14 = π ((1+x)² – 1)² x 0.4 ⇒ x = 5 m ∴ Height of the embankment, x = 5cm

A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to form and embankment of height 40 cm. Find the width of the embankment.

Answer»

Let us assume shape of well is like a solid circular cylinder

Radius of cylinder, r = 2/2 = 1m

Depth(height) of well, h = 14m

Volume of right circular cylinder, V’ = πr² h

=\(π\times{1}^2\times14\)---------(I)

Given that,

length of embankment, l = 40 cm

Let width of the embankment be x m

Volume of the embankment, V’’ = π^r2 h

= π ((1+x)² – 1)² x 0.4 -----------(II)

Since well is spread evenly to form the embankment, so their volumes, V’ = V’’

⇒ π × 14 = π ((1+x)² – 1)² x 0.4

⇒ x = 5 m

∴ Height of the embankment, x = 5cm