Question

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.

Answer 1

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

Radius of cylinder, r = 3.5/2 = 1.75 m 

Depth of well, h = 16 m 

Volume of right circular cylinder, V’ = πr² h

= \(\frac{22}{7}\times{1.75}^2\times16\)---------(I) 

Given that, length of platform, l = 27.5 cm 

Breadth of the platform, b = 7 cm 

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’’

⇒ \(\frac{22}{7}\times({1.75})^2\times16\) = 192.5x

⇒ x = 0.8 m 

∴ Height of the platform = 80 cm