Question

If the radii of the circular ends of a conical bucket which is $45cm$ high are $28cm$ and $7cm$, find the capacity of the bucket (Use $\pi =22/7$)

Answer 1

Clearly, bucket forms a frustum of a cone such that the radii of its circular ends are $r_1=28cm,r_2=7cm$ and height $h=45m$.

Therefore the capacity of the bucket = volume of the frustum

Capacity of the bucket

$=\frac{1}{3}\pi h(r_1^2+r_2^2+r_1{r}_2)$

$=\frac{1}{3}\times \frac{22}{7}\times 45({28}^2+7^2+28\times 7)$

$=22\times 15\times (28\times 4+7+28)$

$=330\times 147{cm}^3$

$=48510{cm}^3$