Question

Type 1 :
Question: Marbles of diameter 1.4cm are dropped into a beaker containing some water and fully submerged. The diameter of the beaker is 7cm. Find how many marbles have been dropped in it if water dries by 5.6cm.
SOLUTION:
HINT: A right-angled cylinder is represented as the below drawn diagram. In this figure “h” represents the height of the cylinder and “r” is the radius of the cylinder. The formula of Volume of cylinder is given by V= . Also no. of objects in it is equal to the Volume of cylinder by Volume of that one object.

The marbles ae always in spherical shape. So, according to the question we have marbles of diameter 1.4 cm. One marble is drawn below.


Since, we know that diameter = 2(radius). Therefore, we have, radius of marble equal to = 0.7cm. Now we will find the Volume of 1 marble= Volume of sphere. It is given by where “r” is the radius of the sphere. Therefore, we have Volume of 1 marble =
Volume of 1 marble =
Now we will consider the diagram of the beaker as shown below and write measurement of height and radius according to the question. Thus, the figure of the beaker containing water is given by,

By the diagram of the beaker containing water, we come to know it’s diameter. Since the diameter is 7cm, therefore we have the radius =or radius = 3.5cm.
The height of the water is 5.6cm as we can see in the diagram. By this value we can find the Volume of the water. This means we can find that how much space the water takes in the beaker. So, by the formula of Volume of water = we have,
Volume of water =
Now we have both the Volume of water and the Volume of the marble. By applying the formula,
No. of marbles dropped in it = Volume of water/ Volume of 1 marble.
No. of marbles dropped in the beaker =
No. of marbles =
No. of marbles =
This is because of the formula
No. of marbles =
No. of marbles =
This is done by the concept that
No. of marbles =
No. of marbles = 150.
Hence, 150 marbles have been dropped into the beaker containing 5.6cm raised water in it.
NOTE: Remember not to get confused between height of the beaker and height of the water inside the beaker. These are two different heights unless it is mentioned in the questions. Don’t forget to use units in the concluding line of the answers if cannot put between solution. Here, the = instead of 3.14, since the calculation is in multiplication.

my question is name the 3 variable in this​

Answer 1

Answer:

Increase in the height of the cylinder due to the sphere, h=3  

9

5

​

=  

9

32

​

 cm

Diameter of sphere =12 cm

Radius of the sphere, R=6 cm

Rise in the volume of water in cylinder = Volume of sphere

πr  

2

h=  

3

4

​

πR  

3

 

r=  

3×32

4×6  

3

×9

​

 

​

 

∴r=9 cm

Therefore, the diameter of the cylindrical vessel =18 cm

Step-by-step explanation: