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A conical vessel is full of water with radius 10 cm and height 54 cm. The water of the vessel poured into a cylindrical vessel having the base radius 15 cm. What will be the depth of the water in the cylindrical vessel? (Assume no water wasted)

A conical vessel is full of water with radius 10 cm and height 54 cm. The water of the vessel poured into a cylindrical vessel having the base radius 15 cm. What will be the depth of the water in the cylindrical vessel? (Assume no water wasted) Correct Answer 8

Given:

The radius of the conical vessel is 10 cm and the height of the vessel is 54 cm.

The radius of the cylindrical vessel is 15 cm.

Concept Used:

If the radius of a cone is ‘r’ cm and height of the cone is ‘h’ then the volume of the cone is (1/3)πr2h

If the radius of the cylinder is ‘r’ and height is ‘h’ then the volume of the cylinder is πr2h

Calculation:

The volume of the water in the conical vessel is (1/3)π × 102 × 54

Let, the depth of water in the cylindrical vessel will be h

The volume of water in the cylindrical vessel is π × 152 × h

Accordingly,

(1/3)π × 102 × 54 = π × 152 × h

⇒ 102 × 18 = 152 × h

⇒ h = (10 × 10 × 18)/(15 × 15)

⇒ h = 8

∴ The depth of the water in the cylindrical vessel will be 8 cm.

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