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Question

The radii of the circles ends of a bucket of height 15 cm are 14 cm and r cm (r < 14 cm).
If the volume of bucket is 5390 cm3, then find the value of r.
[Use π=227]

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Solution

Height of the bucket (which is in the shape of a frustum of a cone), h = 15 cm

Radius of one end of bucket, R = 14 cm

Radius of the other end of the bucket is r.

It is given that the volume of the bucket is 5390 cm3.
13π(R2+r2+Rr)h=5390
13×227×[142+r2+14r]×5390
196+r2+14r=5390×722×5=343
r2+14r+196343=0
r2+14r147=0
r2+21r7r147=0
r(r+21)7(r+21)=0
(r+21)(r7)=0
r70 or r+21=0
r=7 or r=21
Since the radius cannot be a negative number, r= 7 cm
Thus, the value of r is 7 cm.


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