Question

7. A conical vessel of base radius 9 cm and height
20 cm is full of water. A part of this water is now
poured into a hollow cylinder, closed at one end,
till the cylinder is completely filled with water. If
the base radius and the height of the cylinder are
6 cm and 10 cm respectively, find the volume of
water which is left in the cone. (Take π = 3.14)


Please solve it step by step I have to submit it please​

Answer 1

Given :

• Radius of cone = 9 cm
• Height of cone = 20 cm
• Radius of cylinder = 6 cm
• Height of cylinder = 10 cm
• The value of π = 3.14

To Find :

• The volume of water which is left in the cone = ?

Solution :

★ First we will find the volume of water in a cone :

→ Volume of cone = ⅓ πr²h

→ Volume of cone = ⅓ × 3.14 × (9)² × 20

→ Volume of cone = ⅓ × 3.14 × 81 × 20

→ Volume of cone = 31.4 × 27 × 20

→ Volume of cone = 3.14 × 540

→ Volume of cone = 1,695.6 cm³

• Hence,the volume of water in a cone is 1,695.6 cm³.

★ Calculating the volume of water in a cylinder :

→ Volume of cylinder = πr²h

→ Volume of cylinder = 3.14 × (6)² × 10

→ Volume of cylinder = 3.14 × 36 × 10

→ Volume of cylinder = 3.14 × 360

→ Volume of cylinder = 1,130.4 cm³

• Hence,the volume of water in a cylinder is 1,130.4 cm³.

★ Now,let's find the volume of water which is left in the cone :

→ Volume of water left in a cone after filling in cylinder = Volume of cone - Volume of cylinder

→ Volume of water left in a cone after filling in cylinder = ⅓ πr²h - πr²h

→ Volume of water left in a cone after filling in cylinder = 1,695.6 - 1,130.4

→ Volume of water left in a cone after filling in cylinder = 565.2 cm³

• Hence,the volume of water which is left in the cone is 565.2 cm³.