Question

A right circular conical vessel whose internal radius is 21 cm and height 15 cm is full of
water. If water is poured into a right circular cylindrical vessel with internal radius 14 cm, find the length of the water rises​

Answer 1

Given:

• Internal radius of circular conical vessel is 21 cm.
• Height of circular conical vessel is 15 cm.
• Internal radius of cylindrical vessel is 14 cm.

To find:

• Length of water rise (height)?

Formula used:

• Volume of cylinder = πr²h
• Volume of cone = 1/3πr²h

Solution:

★ According to the Question:

• Water is poured from right circular conical vessel full of water into a right circular cylindrical vessel.

We know that,

• Volume of water = Volume of conical vessel.

Therefore,

☯ Volume of water in conical vessel = Volume of water in cylindrical vessel

Now, Putting values,

⇒ 1/3 × 22/7 × 21² × 15 = 22/7 × 14² × h

⇒ 1/3 × 21 × 21 × 15 = 14 × 14 × h

⇒ 2205 = 196 × h

⇒ h = 2205/196

⇒ h = 11.5 cm

∴ Hence, length of water rise in cylindrical vessel is 11.5 cm.

Answer 2

♧Answer♧

Volume of water in the conical vessel will be equal to the volume of water in the cylindrical vessel.

Volume of a Cylinder of Radius "R" and height "h" = πR²h

Volume of a cone = 1/3πr²h,

where r is the radius of the base of the cone and h is the height.

Hence,

22/7×14×14×h = 1/3×22/7×21²×15

196h = (1/3)×6,615

196h = 2205

196h = 2205

h = 2205/196

h = 11.25

Hence, length of water rise in cylindrical vessel is 11.25 m.