A 16 m deep well with diameter 3.5 m is dug up and the earth from it is spread evenly to form a platform 27.5 m by 7 m. Find the height of the platform.
Let us assume shape of well is like a solid right circular cylinder
Radius of cylinder, r = 3.5/2 = 1.75m
Depth of well, h = 16m
Volume of right circular cylinder, V’ = π r2 h
---------(I)
Given that, length of platform, l = 27.5 cm
Breadth of the platform, b = 7cm
Let height of the platform be x m
Volume of the rectangle, V’’ = lbh
= 27.5 × 7 × x
= 192.5x -----------(II)
Since well is spread evenly to form the platform, so volume V’ = V’’
⇒ x = 0.8m
∴ Height of the platform = 80cm