?marbles of diameter 1.4 cm are dropped into a cylindrical vessel of diameter 7 cm containing sone water find the number of marbles drop so that the water lavel rises by 5.6cm

Question

Answer

Solution :

Diameter of the Spherical ball ( d ) = 1.4cm

radius of the ball ( r ) = d/2

r = 0.7 cm

Volume of the Sphere = ( 4/3 )πr³ cm³

v = ( 4/3 ) π ( 0.7 )³ ----( 1 )

ii ) Diameter of the cylinder ( D ) = 7cm

radius of the cylinder ( R ) = D/2

R = 7/2 cm

Suppose water level rises by h= 5.6 cm

in the cylindrical beacker .

Then ,

Volume of the cylinder of height

h = 5.6 cm and radius 7/2 cm

V = πR²h

V = [ π ×( 7/2 )² × 5.6 ]cm³ ----( 2 )

Let the number of balls dropped in the

beaker = n

n = V /v

n = [π ×(7/2)²×5.6cm³]/ [4/3×π×(0.7)³cm³]

after cancellation ,we get

n = 150

Answer

The answer will be approx 150 marbles.
Here, we see in this question,, there is a cylindrical vessel and spherical marbles...
so, we have,,
• volume of cylindrical vessel =πr²h. (π=22/7)
radius(r)=7/2=3.5cm, height(h)=5.6cm.
•volume of spherical marble =4/3πr³(r=14/2=0.7cm)
therefore, the no. of marbles =the volume of cylindrical vessel /the volume of spherical marble
=(22/7* 3.5 * 3.5 * 5.6 )÷ (4/3 * 22/7 * 14/2 * 14/2 * 14.2) =approx 150 marble.

Answer

Problem:
Marbles of diameter 1.4 cm are dropped into a cylindrical vessel of diameter 7 cm containing some water. We need to find the number of marbles required to be dropped in order to make the water level rise by 5.6 cm.

Solution:

Step 1: Calculating the volume of a single marble:
The volume of a sphere (marble) can be calculated using the formula:
V = (4/3) * π * r^3

Given that the diameter of the marble is 1.4 cm, the radius (r) can be calculated as half of the diameter:
r = 1.4 cm / 2 = 0.7 cm

Substituting the value of the radius into the formula, we can calculate the volume of a single marble:
V = (4/3) * π * (0.7 cm)^3
V ≈ 1.437 cm^3

Step 2: Calculating the volume of water displaced by one marble:
The volume of water displaced by one marble is equal to the volume of the marble itself. Therefore, the volume of water displaced is approximately 1.437 cm^3.

Step 3: Calculating the number of marbles required:
To find the number of marbles required to raise the water level by 5.6 cm, we need to calculate the total volume of water displaced by the marbles.

The volume of a cylinder can be calculated using the formula:
V = π * r^2 * h

Given that the diameter of the cylindrical vessel is 7 cm, the radius (r) can be calculated as half of the diameter:
r = 7 cm / 2 = 3.5 cm

Substituting the radius and the height (5.6 cm) into the formula, we can calculate the volume of water displaced by the marbles:
V = π * (3.5 cm)^2 * 5.6 cm
V ≈ 218.27 cm^3

To find the number of marbles required, we divide the total volume of water displaced by the volume of water displaced by one marble:
Number of marbles = 218.27 cm^3 / 1.437 cm^3 ≈ 152.02

Answer:
Therefore, approximately 152 marbles need to be dropped into the cylindrical vessel in order to make the water level rise by 5.6 cm.

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