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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]
Solution
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.
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