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Question
A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.
Solution
According to the question,
The bucket is in the form of frustum of a cone.
We know that,
Volume of frustum of a cone = `1/3 π"h"("r"_1^2 + "r"_2^2 + "r"_1"r"_2)`, where, h = height, r1 and r2 are the radii (r1 > r2)
For bucket,
Volume of bucket = 28.490 L
1 L = 1000 cm3
Volume of bucket = 28490 cm3
Radius of top, r1 = 28 cm
Radius of bottom, r2 = 21 cm
Let the height = h.
Substituting these values in the equation to find the volume of bucket,
We have,
Volume of bucket = `1/3 π"h"[28^2 + 21^2 + 28(21)]`
28490 = `1/3 xx 22/7 xx "h"(784 + 441 + 588)`
= `22/7 xx "h" xx 1813`
⇒ h = `(28490 xx 21)/(22 xx 1813)`
⇒ h = 15
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