Question

A+solid+spherical+ball+of+radius+6cm+is+melted+and+recast+into+64+identical+spherical+marbles.+Find+the+radius+of+each+marble

Answer 1

Answer:

Volume of the solid spherical ball= 4/3*22/7*6*6*6

Volume of 64 identical spherical marbles = 64*4/3*22/7*r^3

ACCORDING TO THE GIVEN QUESTION,

4/3*22/7*6*6*6 = 64*4/3*22/7*r^3

=》6*6*6 = 64*r^3

=》r^3 = (6*6*6) / 64

AFTER REDUCING THE LEFT HAND SIDE BY 2

=》r^3 = (3*3*3)/8

AFTER DOING CUBE ROOT OF THE LEFT HAND SIDE

=》r = 3/2

Radius of each spherical marble =3/2 =1.5 cm

Answer 2

Radius of each marble is 1.5 cm

Question: A solid spherical ball of radius 6 cm is melted and recast into 64 identical spherical marbles. Find the radius of each marble.

Solution:

Given that, radius of the solid ball is 6 cm.

Then the volume of the ball is

= 4/3 * π * (radius)³

= 4/3 * π * 6³ cm³

Also given that, the solid ball is melted and recast into 64 identical marbles. Let radius of each marble be r cm.

Then the volume of the solid ball equals to the total volume of 64 marbles. i.e.,

4/3 * π * 6³ = 64 * 4/3 * π * r³

or, 6³ = 64 * r³

or, 6³ = 4³ * r³

or, 4r = 6 (taking cubic root to both sides)

or, r = 6/4

or, r = 1.5

Therefore radius of each marble is 1.5 cm.

Related question:

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball. - https://brainly.in/question/2313953