Understanding Volume: Calculating How Much Soup a Can Holds

    Let's dive into a practical math problem that not only tests your arithmetic reasoning skills but also brings some fun along the way. How much soup can a can hold if it’s six inches high with a diameter of 4 inches? The options are pretty tantalizing: 50.27 in³, 60.44 in³, 75.36 in³, or 80.00 in³. If you’re scratching your head a bit, don’t worry; it’s all about understanding a straightforward formula.

    First off, we’re dealing with a cylinder, and the really cool thing is that calculating its volume is as easy as pie—specifically, pi! The formula for the volume \( V \) of a cylinder is:

    \[
    V = \pi r^2 h
    \]

    Here’s what you need to know: \( r \) represents the radius of the base of the can, and \( h \) is its height. In our scenario, the height \( h \) is 6 inches. But wait, the diameter of our can is 4 inches. So, to find the radius, we chop that diameter in half:

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

    Now, let’s plug in those values into the trusty volume formula. It’s simple math, and we’ve got this!

    \[
    V = \pi (2 \text{ inches})^2 (6 \text{ inches})
    \]

    When we tackle the area of the base, we find:

    \[
    (2 \text{ inches})^2 = 4 \text{ square inches}
    \]

    It’s like building blocks; you find the area first, and then you multiply by height to get the volume. So, inserting that into our equation,

    \[
    V = \pi \times 4 \text{ in}^2 \times 6 \text{ in}
    \]

    Now, if you do the math, you end up with:

    \[
    V = 24\pi
    \]

    Now here comes the cool part—how do we convert that into something more usable, like in³? Since we know \( \pi \) is approximately 3.14, we either do the multiplication or just pull out our calculators (hey, we all need some tech help sometimes!). This leads us to:

    \[
    V \approx 75.36 \text{ in}^3
    \]

    So, the answer to our soup can question is C. 75.36 in³. Yes, you did it! 

    But why is this little math exercise so important? Well, for anyone gearing up for the AFCT, arithmetic reasoning isn’t just about numbers; it’s about understanding the world around you. Each problem helps hone critical thinking skills that are essential in both military service and everyday life. 

    Remember, practice makes perfect! By engaging with problems like this one, you’re building a solid foundation in math that will boost your confidence and prepare you for the challenges that lie ahead. And honestly, who doesn’t want to impress their friends with their newfound math skills? 

    So, grab that can of soup (even if it’s just a metaphor for something bigger) and start calculating. You never know when those math skills will come in handy—perhaps at a dinner party where you have to figure out how many people you can serve! Keep at it, and you’ll find that arithmetic reasoning can be both fun and immensely satisfying.