A 4" x 1-1/4" round box has how many cubic inches of fill space area?

To determine the fill space area of a round box, it's essential to understand how to calculate the volume of a cylinder. The formula for the volume ( V ) of a cylinder is given by:

[ V = \pi r^2 h ]

where ( r ) is the radius and ( h ) is the height.

In this question, the dimensions of the round box are given as 4 inches in diameter and 1-1/4 inches in height. First, we need to convert the diameter to the radius. The radius ( r ) is half the diameter, so:

[ r = \frac{4 \text{ inches}}{2} = 2 \text{ inches} ]

The height ( h ) is given as 1-1/4 inches, which can be converted to a decimal for easier calculation:

[ h = 1 \text{ inch} + 0.25 \text{ inches} = 1.25 \text{ inches} ]

Now we can substitute these values into the volume formula:

[ V = \pi (2 \text{ inches})^2 (1.25 \text{ inches}) ]

Calculating the radius squared:

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