Question

Total volume of 21 steel balls in a bearing is 88 cm3. Find the diameter of each ball

Answer 1

Step-by-step explanation:

21×4/3π×r^3=88

7×5π×r^3=88

7×5×22/7×r^3=88

r^30

35/7×r^3=4

5×r^3=4

r^3=4/5

r=3√4/5

d=2×3√4/5

Answer 2

The diameter of each ball is 2 cm.

Given : Total volume of 21 steel balls in a bearing is 88 cm3.

To find : The diameter of each ball.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the diameter of each ball)

Now,

Volume of a sphere = (4/3) × π × (radius)³

Let, radius of each ball = r cm

So,

Volume of a ball (spherical in shape) :

= [(4/3) × π × (r)³] cm³

And,

Volume of 21 balls :

= [21 × (4/3) × π × (r)³]

= 28πr³ cm³

According to the data mentioned in the question,

14πr³ = 88

28 × (22/7) × (r)³ = 88

88 × r³ = 88

r³ = 88/88

r³ = 1

r = 1

The radius of one ball = 1 cm

So,

The diameter of the ball = 2 × radius = 2×1 = 2 cm

Hence, the diameter of the ball is 2 cm