Question

how many balls each of radius 3cm can be made from a solid sphere of lead to radius 27cm​

Answer 1

Answer:

729 balls

Step-by-step explanation:

no of balls= vol of solid sphere / vol of

ball

$= \frac{4}{3} \pi { r}^{3} \div \frac{4}{3} \pi {r}^{3}$

$= {27}^{3} \div {3}^{3}$

$= 27 \times 27 \times 27 \div (3 \times 3 \times 3)$

=27×27

= 729

Answer 2

729 balls can be made.

Given : Radius of all spherical ball is 3 cm and radius of bigger solid spherical ball of radius 27cm.

To find : The number of smaller balls that can be made from the bigger solid ball.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of smaller balls)

We know that,

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

So,

Volume of a smaller ball = [(4/3) × π × (3)³] cm³

And,

Volume of the bigger solid ball = [(4/3) × π × (27)³]cm³

Now,

The number of smaller balls :

= Volume of the bigger solid ball ÷ Volume of a smaller ball

= [(4/3) × π × (27)³] ÷ [(4/3) × π × (3)³]

= (27)³ ÷ (3)³

= 729

(This will be considered as the final result.)

Hence, 729 balls can be made