Question

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.

Answer 1

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

`rArr 1/3 pi"h"("R"^2 + r^2 + Rr)=5390  "cm"^3`

`rArr 1/3 xx 22/7xx15xx(14^2+r^2+14r) = 5390`

`= 110/7xx(196+r^2+14r)=5390`

`rArr 196 + r^2+14r=(5390xx7)/110`

`rArr 196 + r^2 + 14r = 343`

`rArr r^2 + 14"r"- 147 = 0`

`rArr r^2 + 21r - 7r-147 = 0`

⇒ r (r + 21)-7(r+21)=0

⇒ (r+21)(r-7)=0

⇒ r + 21 = 0 or r = 7

As, cannot be negative

∴ r = 7 cm

So the value of r is 7