Question

A cylindrical bucket, 44, cm high and having radius of base 21 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap as 33 cm, find the radius and the slant height of the heap.

Answer 1

The height of the conical heap is $33cm$

The height of cylindrical bucket $44cm$

The radius of cylindrical bucket $21cm$

The volume of sand it can hold

$=\pi r^{2}h=\frac{22}{7}\times 21\times 21\times 44=22\times 3\times 21\times 44=66\times 21\times 44=60,984$

So the volume of conical heap is $60984$

$⟹\frac{1}{3}\times \pi r^{2}h=60984\frac{1}{3}\times \frac{22}{7}\times r^2\times 33=60984r^2=60984\times 3\times \frac{7}{22}\times \frac{1}{33}{r}^2=1764r=\sqrt{1764}=42$

According to pytagorous theorm

${\left(Slantheight\right)}^2={\left(radius\right)}^2+{\left(height\right)}^2$

${\left(Slantheight\right)}^2={42}^2+{33}^2$

${\left(Slantheight\right)}^2=1764+1089$

${\left(slantheight\right)}^2=2853$

slant height$=\sqrt{2853}$

slant height$=53.41$cm