A cylinder container has a radius of 3 in. and a height of 12 in. The cylinder contains 25 spherical balls that have a diameter of 1.5 in. About how much space is left in the container not including the balls?

Sure, let's solve this step by step.

Step 1: Calculate the volume of the cylinder container. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. So, V = π * (3 in)² * 12 in = 108π cubic inches.

Step 2: Calculate the volume of one spherical ball. The formula for the volume of a sphere is V = 4/3πr³, where r is the radius. The radius of the ball is half of the diameter, so r = 1.5 in / 2 = 0.75 in. So, V = 4/3 * π * (0.75 in)³ = 1.77π cubic inches.

Step 3: Calculate the total volume of the balls. The total volume of the balls is the volume of one ball multiplied by the number of balls. So, V = 25 * 1.77π cubic inches = 44.25π cubic inches.

Step 4: Calculate the remaining volume in the cylinder. The remaining volume is the volume of the cylinder minus the total volume of the balls. So, V = 108π cubic inches - 44.25π cubic inches = 63.75π cubic inches.

So, there is approximately 63.75π cubic inches of space left in the container not including the balls.

Sure, let's solve this step by step.

Step 1: Calculate the volume of the cylinder container. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.

So, V = π * (3 in)² * 12 in = 108π cubic inches.

Step 2: Calculate the volume of one spherical ball. The formula for the volume of a sphere is V = 4/3πr³, where r is the radius.

The radius of the ball is half of the diameter, so r = 1.5 in / 2 = 0.75 in.

So, V = 4/3 * π * (0.75 in)³ = 1.77π cubic inches.

Step 3: Calculate the total volume of the balls. The total volume of the balls is the volume of one ball multiplied by the number of balls.

So, V = 25 * 1.77π cubic inches = 44.25π cubic inches.

Step 4: Calculate the remaining volume in the cylinder. The remaining volume in the cylinder is the volume of the cylinder minus the total volume of the balls.

So, V = 108π cubic inches - 44.25π cubic inches = 63.75π cubic inches.

Therefore, about 63.75π cubic inches of space is left in the container not including the balls.