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.