Question

Question 3
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

Given, volume of the frustum $=28.49L=28.49\times 1000c{m}^3[\because 1L=1000c{m}^3]$
$=28490c{m}^3$

Radius of the top $\left(r_1\right)=28cm$
Radius of the bottom $\left(r_2\right)=21cm$

Let height of the bucket = h cm
Now, volume of the bucket
$=\frac{1}{3}\pi h(r_1^2+r_2^2+r_1{r}_2)=28490\left[given\right]$

$\Rightarrow \frac{1}{3}\times \frac{22}{7}\times h({28}^2+{21}^2+28\times 21)=28490\Rightarrow h(784+441+588)=\frac{28490\times 3\times 7}{22}\Rightarrow 1813h=1295\times 21\therefore h=\frac{1295\times 21}{1813}=\frac{27195}{1813}=15cm$