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Question
A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm3 . the radii of the top and bottom of the circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the bucket and also the area of the metal sheet used in making it.
Solution
Let the height of the bucket ne h cm and Slant height be I cm.
Here,
r1 = 20 cm
r2 = 12 cm
And capacity of bucket = 12308.8 cm3
We know that capacity of bucket = `(pi"h")/3 (r_2^2 + r_2^2 + r_1r_2)`
`= 3.14 xx "h"/3 (400 + 144 + 240)`
`= 3.14xx"h"/3 xx 784`
So we have = `3.14xx"h"/3xx784` = 12308.8
`"h" = (12308.8xx3)/(3.14xx784)`
= 15 cm
Now, the slant height of the frustum,
l = `sqrt("h"^2 + ("r"_1 - "r"_2)^2`
`= sqrt(15^2 + 8^2)`
`=sqrt289`
= 17 cm
Area of metal sheet used in making it
`= pir_2^2 + pi(r_1 + r_2)^2`
`= 3.174 xx [144 + (20 + 12) xx 17]`
= 2160.32 cm2
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