Question

spherical marbles are dropped into a fish tank. Each marble is 60 cm in volume. How much water would overflow if 480 marbles are dropped in the tank

Answer 1

Answer:

5.6cm

Step-by-step explanation:

diameter of the spherical marble = 1.4 cm

radius of the marble= 0.7 cm

volume of each marble =3/4$\pi$r^3

=3/4*7/22*(0.7)^3

=1.14

volume of 150 marbles =1.14*150

=216cm^3

Let the rise in level of water in then cylindrical vessel=h cm

diameter of vessel=7cm

radius of vessel = 3.5 cm

volume of increased level of water=$\pi$r^2

=7/22*3.5*3.5*h

volume of rise in level of water=volume of 150 marbles

7/22*3.5*3.5*h=216cm^2

h=5.6cm

Therefore the rise of level of water =5.6cm

Answer 2

Given,

The volume of each spherical marble dropped into the fish tank = 60 cm^3

Total number of marbles dropped into the tank = 480

To find,

Amount of water that will overflow.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically, according to the Archimedes' principle;

If the body is completely submerged in a fluid, then the volume of fluid displaced is equal to the volume of the body.{Statement-1}

According to the question;

The volume of each spherical marble = 60 cm^3

So, the volume of all 480 marbles dropped into the tank

= 480 × (volume of each spherical marble)

= 480 × 60 cm^3

= 28,800 cm^3

Now, according to the statement-1;

Amount of water that will overflow from the tank

= the volume of all 480 marbles dropped into the tank

= 28,800 cm^3

Hence, 28,800 cm^3 amount of water will be displaced from the tank.