Question

How many spherical balls of diameter 1 CM can be completely submerged in a cone of diameter 5 cm and height 4.5cm.explain about your solution method

Answer 1

Answer:

Step-by-step explanation:

We know that the volume of cone = $\frac{\pi r^2{h} }{3}$

= 29.45 cube.cm.

(Here h is the height of the cone and r is the radius of the cone which is diameter/2)

Volume of sphere is = $\frac{4\pi x^{3} }{3}$;

Volume of sphere = 4.19 cube cm.

Suppose n number of spherical balls are submerged in to the cone:

so that the number of balls = 29.45/4.19 = 7.02;

Here we will consider the only integer value with out fraction

It means 7 spherical balls are submerged in to the cone

Answer 2

Answer:

Number of spherical balls that can be completely submerged  = 56

Step-by-step explanation:

As, volume of cone  = πr²h/3

where, r = radius of cone = 5/2 cm = 2.5 cm

            h = height of cone = 4.5 cm

Thus, volume of cone = π * 2.5 * 2.5 * 4.5/3

                                    =  9.375π  cm³

Volume of a spherical ball =  4/3 * πR³

                                            = 4/3 * π * 0.5 * 0.5 * 0.5

                                            = (0.5/3)π  cm³

As, when we submerge spherical balls in cone , the level of liquid rises in the cone . So, volume of liquid that is overflown is equal to volume of spherical balls .

Thus, number of spherical balls that can be completely submerged in the cone  =  volume of cone/Volume of a spherical ball

         =  9.375π/[(0.5/3)π]

          =  56  approx