The slant height of a bucket is 26 cm. The diameter of upper and lower circular ends are 36 cm and 16 cm. Find the height of the bucket.

It is given that the slant height of a bucket is 26 cm and the diameter of upper and lower circular ends are 36 cm and 16 cm. We need to find the height of the bucket.

It is known that the bucket is in the form of the frustum and the slant height of the frustum is given by the relation

${\mathrm{l}}^2={\mathrm{h}}^2+(\mathrm{R}-\mathrm{r}{)}^2$, where

l is the slant height,

h is the height of the frustum, 

R is the radius of upper circular end and

r is the radius of the lower circular end.

On substituting the values, we get the height of the bucket as

$\begin{array}{l}\Rightarrow {\mathrm{l}}^2={\mathrm{h}}^2+(\mathrm{R}-\mathrm{r}{)}^2\\ \Rightarrow {26}^2={\mathrm{h}}^2+(18-8{)}^2\\ \Rightarrow 676={\mathrm{h}}^2+(10{)}^2\\ \Rightarrow 676={\mathrm{h}}^2+100\\ \Rightarrow {\mathrm{h}}^2=576\\ \Rightarrow \mathrm{h}=24\mathrm{cm}\end{array}$

Hence, the height of the bucket is 24 cm.