lincoln is filling a cylindrical shaped box woth sphere shaped balls. the box has a radius of 5 inches and a height of 10 inches. each ball has a radius of 2 inches. how many balls can fit into the box? round down to the nearest whole number.

Answer 1

To determine how many balls can fit into the box, we first need to calculate the volume of the box and the volume of a single ball.

The volume of the box can be calculated using the formula for the volume of a cylinder:

V_box = π * r^2 * h

Where:
- V_box is the volume of the box,
- π is a mathematical constant, approximately equal to 3.14159,
- r is the radius of the box (5 inches), and
- h is the height of the box (10 inches).

V_box = 3.14159 * 5^2 * 10
V_box = 3.14159 * 25 * 10
V_box = 3.14159 * 250
V_box ≈ 785.39875 cubic inches

Next, we calculate the volume of a single ball using the formula for the volume of a sphere:

V_ball = (4/3) * π * r^3

Where:
- V_ball is the volume of a single ball, and
- r is the radius of the ball (2 inches).

V_ball = (4/3) * 3.14159 * 2^3
V_ball = (4/3) * 3.14159 * 8
V_ball = (4/3) * 25.13272
V_ball = 33.510321 cubic inches

Finally, we divide the volume of the box by the volume of a single ball to find the number of balls that can fit:

Number of balls = V_box / V_ball
Number of balls ≈ 785.39875 / 33.510321
Number of balls ≈ 23.446

Since we need to round down to the nearest whole number, we can conclude that approximately 23 balls can fit into the box.