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 $c{m}^3$, find the value of r.

Answer 1

Given: height of the bucket (h) = 15 cm

$r_1$ = 14 cm and $r_2$ = r cm

Now, volume of bucket = $\frac{\pi }{3}$ [$r_1^2$ + $r_2^2$ + $r_1{r}_2$]h

$\Rightarrow$ $\frac{22}{3\times 3}$ [${14}^2$ + $r^2$ + 14r]

$\Rightarrow$ $r^2+14r+196$ = $\frac{5390\times 7}{110}$

$\Rightarrow$ $r^2+14r+196$ = 343

$\Rightarrow$ $r^2+14r-147$ =0

$\Rightarrow$ $r^2+21r-7r-147$ =0

$\Rightarrow$ (r-7) (r+21) = 0

$\Rightarrow$ r = 7 or r = -21

Since, r cannot be negative

So, the value of r is 7 cm.