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
Answers
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♧
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.