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A cylindrical bucket of radius 96 cm and height 54 cm is filled with sand. The bucket is emptied on the ground and a conical heap of base radius x cm is formed. If the height of the heap is 72 cm, then what is the value of x?
1. 108
2. 196
3. 144
4. 120

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Correct Answer - Option 3 : 144

Given:

Sand in a cylindrical vessel is poured in a conical vessel. 

Radius is 96cm and Height is 54 cm of a cylindrical bucket.

Height of conical heap is 72 cm and radius is x cm

Concept Used:

Volume of a cylindrical vessel = Volume of a conical vessel

Formula Used:

Volume of a cylinder = πR2H,

Volume of a cone = 1/3πr2h,  

Where,

R is a radius of a cylinder,

r is a radius of a cone,

H is a height of a cylinder,

h is a height of a cone

Calculation:

According to the question,

⇒ πR2H = 1/3πr2h

⇒ π × (96)2 × 54 = 1/3 × π × (x)2 × 72

⇒ 96 × 96 × 54 × 3 = x2 × 72

⇒ x2 = (96 × 96 × 54 × 3)/72

⇒ x2 = 20,736

⇒ x = √20,736 = 144

∴ The value of a x is 144 m. 

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