Question

A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. ( = ). 3 marks

Answer 1

Given :

• Radius of a Conical vessel (r) = 5cm
• Height of a Conical vessel (h) = 24cm
• Radius of a Cylindrical vessel (R) = 10cm

To Find :

• The height to which the water will rise in the cylindrical vessel.

Solution :

Let H be the height of water rise in a Cylindrical vessel.

⠀

⟹ Volume of Conical vessel = ⅓ πr²h

• Volume = ½ π(5)² (24) cm³

⟹ Volume of Cylindrical vessel = πR²H

• Volume = π(10)² H cm³

⠀

It is given that :

• Water in Conical vessel is emptied into a cylindrical vessel.

⟼ ⅓ π (5)² (24) = π (10)² H

⟼ ⅓ × π × 25 × 24 = π × 100 × H

⟼ ⅓ × 25 × 24 = 100 × H

⟼ 25 × 8 = 100 × H

⟼ 200 = 100 × H

⟼ 200 / 100 = H

⟼ 2cm = H

Hence, The Height of the water rise in the Cylindrical vessel is 2cm

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Answer 2

★ Given :

• A conical vessel, with base radius 5 cm and height 24 cm, is full of water.

• This water is emptied into a cylindrical vessel of base radius 10 cm.

★ To find :

• The height to which the water will rise in the cylindrical vessel.

★ Solution :

• In the question It's given that water is emptied into a cylinderal vessal.

• By the formula of Volume of cone and The volume of cylinder, We can find the height in which the water will rise in the cylindrical vessel.

✰ Radius of Conical Vessal = 5cm

✰ Height of Conical Vessal = 24cm

✰ Radius of Cylinderal Vessal = 10cm

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Let's Find out...!

Volume of cone = Volume of cylinder

1/3πr²h = πr²h

➤ 1/3 × π × (5)² × 24 = π × (10)² × H

➤ 1/3 × 25 × 24 = 100 × H

➤ 25 × 8 = 100 × H

➤ H = 25 × 8/100

➤ H = 200/100

➤ H = 2 cm

∴ Height in which water is raised in cylindrical vessel is 2cm.

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