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Question
A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, then find the height of the bucket.
Solution
We have,
Radius of upper end, R=28 cm and
Radius of lower end, r = 21 cm
Let the height of the bucket be h.
Now,
Volume of water the bucket can hold = 28.49 L
⇒ Volume of bucket = 28490 cm3 (As, 1L = 1000 cm3)
`rArr 1/3pi"h"("R"^2+"r"^2+"Rr") = 28490`
`rArr 1/3xx22/7xx"h"(28^2+21^2+28xx21) = 28490`
`rArr (22"h")/21xx49xx(16+9+12)=28490`
`rArr (22"h")/3 xx7xx37 = 28490`
`rArr "h" = (28490xx3)/(22xx7xx37)`
∴ h = 15 cm
So, the height of the bucket is 15 cm.
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