# A cylindrical buc

Given.

Height of bucket is 44 cm

Radius of bucket is 21 cm

Height of conical heap is 33 cm

Formula used/Theory.

Volume of cylinder = πr2h

Volume of cone = πr2h

Let the Radius of conical heap be x

Volume of bucket = πr2h

= π × (21 cm)2 × 44 cm

= 19404π cm3

Volume of conical heaps = πr2h

= π × x2 × 33 cm

= 11π × x2 cm

**Note we will not put value of π as it will be divided in next step

As we put bucket of sand on ground it will form a conical heap volume of conical heaps will be equal to volume of bucket

equating both we will get the Radius of conical heap

Volume of bucket = Volume of conical heaps

11π × x2 cm = 19404π cm3

x2 = x2 = 1764 cm2

x = √ (1764 cm2)

x = 42 cm

Radius of conical heap is 42 cm

In cone;

As the radius , height and slant height makes Right angled triangle where hypotenuse is slant height

Then by Pythagoras theorem

(Slant height)2 = (height)2 + (radius)2

(Slant height)2 = (33 cm)2 + (42 cm)2

(Slant height)2 = 1089 cm2 + 1764 cm2

(Slant height)2 = 2853 cm2

Slant height = √(2853 cm2)

= 53.41 cm

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