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 = πR^{2}H,

Volume of a cone = 1/3πr^{2}h,

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 = x^{2} × 72

⇒ x2 = (96 × 96 × 54 × 3)/72

⇒ x2 = 20,736

⇒ x = √20,736 = 144

**∴ The value of a x is 144 m.**