A vessel is in the form of an inverted cone. It's height is 11cm and the radius of its top which is open is 2.5cm. It is filled with water upto the rim. When lead shots each of which is a sphere of radius 0.25cm are dropped into the vessel. 2/5 of the water flows out. Find the number of lead shots dropped into the vessel
Answers
Answer:
- Number of lead shots dropped = 440
Given:
- Height of the conical vessel = 11 cm
- Radius of the top of the vessel = 2.5 cm
- Radius of the lead shots = 0.25 cm
When 'n' number of balls are dropped inside the vessel, 2/5 th of the volume flows outside the vessel.
To Find:
- n = ?
Steps:
Hence let's first calculate the volume of the conical vessel.
Volume of the sphere is calculated as:
Amount of volume displaced = 2/5th of Vessel Volume.
We know that,
Volume Added = Volume Displaced
Hence writing in terms of equation we get:
→ n × Volume of 1 lead shot = 2/5th Volume of Cone
Hence the number of lead shots dropped into the vessel is 440.
Given that -
A vessel is in the form of an inverted cone.
Vessel (cone) height = 11 cm
The radius of it's (vessel) (cone) top which is open = 2.5 cm.
Lead shots each of which is a sphere of radius 0.25cm are dropped into the vessel.
(Radius of lead shots = 0.25 cm)
2/5 of the water flows out.
To find -
The number of lead shots dropped into the vessel.
Solution -
440 are the number of lead shots dropped into the vessel.
Using concepts -
Formula to find volume of cone.
Formula to find volume of sphere.
Using formula -
Where,
● Value of π is or 3.14
● π pronounced as pi
● r denotes radius
● h denotes height
Full solution -
~ Let us find the volume of vessel firstly,
Henceforth,
~ Let us find the volume of lead shots
Henceforth,
~ Now as the question says that 2/5 of the water flows out or this is the displaced volume.
⚔ So, now as we already know that volume added = volume displaced
⚔ Henceforth, the formed equation is
x × 0.0654 = × 71.95
⚔ Here,
↗️ x is assumption at the place of the number of lead shots dropped into the vessel
↗ 0.0654 is volume of lead shots
↗ is flow out volume
↗ 71.95 is volume of vessel
x × 0.0654 = 28.78
x =
x = 440
The lead shots dropped into the vessel = 440