Question

A conical flask of height 24 cm is full of water . If this water is poured into another cylindrical flask of radius half of conical flask , then how much water level of the cylindrical flask will be raised ?​

Answer 1

Answer:

$\bigstar{\bold{Level\:of\:water=32\:cm}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Height of conical flask (h₁) = 24 cm
• Radius of cylindrical flask (r₂) = 1/2 × r₁

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The level of water raised in the cylindrical flask

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ The volume of water in the flask = Volume of cone

→ Volume of a cone is given by the formula,

  Volume of a cone = 1/3 π (r₁)² h₁

→ Substitute the datas,

   Volume of a cone = 1/3 × 3.14 × (r₁)² × 24

   Volume of a cone = 25.12 (r₁)²

→ Hence volume of water in the flask = 25.12 (r₁)² cm³

→ Now volume of water in the cylinder =  Volume of cylinder

→ Volume of a cylinder is given by

  Volume of a cylinder = π (r₂)² h₂

  Here r = r₁/2

  Volume of cylinder = 3.14 × (r₁)²/4 × h₂

→ We know that volume of water = 25.12 (r₁)²

→ Hence

  25.12 (r₁)² = 3.14 × (r₁)²/4 × h₂

→ Cancelling (r₁)² on both sides

   25.12 = 3.14  × 1/4 × h₂

   h₂ = 25.12 × 4/3.14

   h₂ = 32 cm

→ Hence the water level would be 32 cm in the cylindrical flask

$\boxed{\bold{Level\:of\:water=32\:cm}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ The volume of a cone = 1/3 × π × r² × h

→ The volume of a cylinder = π × r² × h