Question

A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm³ of water. The radii of the top and bottom circular ends are
20 cm and 12 cm, respectively. Find the height of the bucket. [Use π = 3.14]

Answer 1

We have, 

Radius of the upper end, R = 20 cm and 

Radius of the lower end , r = 12 cm

Let the height of the bucket be h.

As,

Volume of the bucket = 12308.8 cm³

`=> 1/3 pi"h" ("R"^2 + r^2 + "Rr") = 12308.8`

`=> 1/3xx3.14xx"h"xx(20^2+ 20xx12) = 12308.8`

`=> (3.14"h")/3xx(400+144+240) = 12308.8`

`=> (31.4 "h")/3xx784=12308.8`

`=> "h" = (12308.8xx3)/(3.14xx784)`

∴ h = 15 cm

So, the height of the bucket is 15 cm.