Question

A bucket is in the form of a frustum of a cone and holds$28.490$ litres of water. The radii of the top and bottom are $28$ cm and $21$ cm, respectively. Find the height of the bucket.

Answer 1

Step-1 : Given data:

Volume of bucket$=28.490L$

Radius of top $r_1=28cm$

Radius of bottom $r_2=21cm$

We know that

$1L=1000c{m}^3$

Volume of bucket$=28490c{m}^3$

Step-2 Voulme of frustrum:

The bucket is in the form of frustum of a cone.

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

Where,

$h=height$

$r_1$ and$r_2$ are the radii($r_1>r_2$)

On substituting these values in the equation to find the volume of bucket, we obtain:

$=\frac{1}{3}\pi h[{28}^2+{21}^2+28(21\left)\right]$

$28490=\frac{1}{3}\times \frac{22}{7}\times h(784+441+588)=\frac{22}{21}\times h\times 1813$ $\left[\because \pi =\frac{22}{7}\right]$

$\Rightarrow h=\frac{(28490\times 21)}{(22\times 1813)}$

$\Rightarrow h=15$
Hence, the height of the bucket $\mathbf{h}\mathbf{=}\mathbf{15}\mathbf{}\mathbf{cm}$