Question

The radii of the circular ends of a bucket of hight 15cm are 14cm and rcm (r<14cm) . If the volume of bucket is 5390cm³,then find the value of r?​

Answer 1

Step-by-step explanation:

The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14). If the volume of bucket is 5390 cm3, then find the value of r.

SOLUTION

We have,

Height, h = 15 cm,

Radius of the upper end, R = 14 cm

Radius of lower end = r,

As,

Volume of the bucket = 5390 cm3

⇒13πh(R2+r2+Rr)=5390 cm3

⇒13×227×15×(142+r2+14r)=5390

=1107×(196+r2+14r)=5390

⇒196+r2+14r=5390×7110

⇒196+r2+14r=343

⇒r2+14r-147=0

⇒r2+21r-7r-147=0

⇒ r (r + 21)-7(r+21)=0

⇒ (r+21)(r-7)=0

⇒ r + 21 = 0 or r=7

As, connot be negative

∴ r = 7 cm

So the value of r is 7

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