Question

A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket. [Use${\displaystyle \pi \frac{22}{7}}$ ]

 

Answer 1

Let the height of the bucket be h cm.

Suppose r₁ and r₂ be the radii of the circular ends of the bucket.

Given, r₁ = 28 cm and r₂ = 21 cm

Capacity of bucket = 28.49 litres

∴Volume of the bucket = 28.49 × 1000 cm³ [1 litre = 1000 cm³]

${\displaystyle \Rightarrow \frac{1}{3}\pi h(r_1^2+r_2^2+r_1{r}_2)=28.49\times 1000c{m}^3}$

${\displaystyle \Rightarrow \frac{1}{3}\times \frac{22}{7}\times h\times [{\left(28\right)}^2+{\left(21\right)}^2+(28\times 21)]c{m}^2=28490}$

${\displaystyle \Rightarrow \frac{22}{21}\times h\times 1813=28490cm}$

${\displaystyle \Rightarrow h=\frac{28940x21}{22\times 1813}cm}$

${\displaystyle h=15cm}$

Thus, the height of the bucket is 15 cm.