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]
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+196−343=0
⇒r2+14r−147=0
⇒r2+21r−7r−147=0
⇒r(r+21)−7(r+21)=0
⇒(r+21)(r−7)=0
⇒r−7−0 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.