how many balls with a diameter of 6 cm. each can a square box hold if the box has a measure of 36 square cm. on each side?

The box is 6 cm by 6 cm by 6 cm.

(you said it was 36 cm^2 for each side)
The ball has a diameter of 6 cm

mmmmh, what do you think?

To find out how many balls with a diameter of 6 cm each can fit inside a square box with sides measuring 36 cm, we need to calculate the volume of the balls and the volume of the box.

1. Volume of a Ball:
The formula to find the volume of a sphere (ball) is given by:
V = (4/3) * π * r^3
where r is the radius (half of the diameter).

Since the diameter is 6 cm, the radius would be 6/2 = 3 cm.
Plugging in the values:
V = (4/3) * π * (3^3)
V = (4/3) * 3.14 * 27
V ≈ 113.04 cm^3

2. Volume of the Square Box:
Since the box is square, all sides measure 36 cm.
Therefore, the volume of the box would be:
V = Side^3
V = 36^3
V = 46,656 cm^3

3. Number of Balls:
To determine the maximum number of balls that can fit inside the box, divide the volume of the box by the volume of each ball.
Number of Balls = Volume of Box / Volume of Each Ball
Number of Balls = 46,656 cm^3 / 113.04 cm^3
Number of Balls ≈ 413.13

Since we cannot have a fraction of a ball, we can fit a maximum of 413 balls with a diameter of 6 cm each inside the square box.

To determine how many balls with a diameter of 6 cm each can fit in a square box, we first need to calculate the volume of one ball and the volume of the box.

The volume of a sphere can be calculated using the formula V = (4/3) * π * r^3, where V represents volume and r represents the radius of the sphere. In this case, the radius is half the diameter, so it is 6/2 = 3 cm. Plugging the values into the formula, we get V = (4/3) * 3.14 * 3^3, which simplifies to V ≈ 113.04 cubic cm.

Next, we need to find the volume of the box. Since it is a square box with sides measuring 36 cm each, the volume can be calculated by cubing the side length: V = 36^3 = 46,656 cubic cm.

To determine how many balls can fit inside the box, we need to divide the volume of the box by the volume of one ball: 46,656 cubic cm / 113.04 cubic cm ≈ 413 balls.

Therefore, a square box with sides measuring 36 cm each can hold approximately 413 balls with a diameter of 6 cm each.