How to determine the weight of a solid aluminum cylinder when you know its diameter, height, and unit weight.

Outline:

• Opening hook: practical math in naval engineering; why a single cylinder matters

• Core problem recap: radius from diameter, volume formula for a solid cylinder, unit weight concept

• Step-by-step walkthrough:

• Convert diameter to radius

• Compute volume with V = π r^2 h

• Plug in numbers and approximate

• Multiply by unit weight to get weight

• Confirm the final figure and a quick check

• Real-world relevance: weight, buoyancy, and how engineers think about metal parts

• Common snags to avoid

• Practical takeaways and nerdy little tangents

• Friendly wrap-up

Weight, math, and naval know-how: a simple cylinder that tells a bigger story

Let me be honest: some of the most useful math lives in quiet, everyday problems. A solid aluminum cylinder, a few quick inches or feet, and a unit weight that seems almost abstract until you need it to size a component or estimate payload. For NAVFAC personnel and students who want to connect theory to real-world numbers, this kind of calculation is a tiny, practical superpower.

Let’s walk through a clean, straightforward example—the kind you’d encounter when you’re checking a component’s weight for a project, or validating a design figure in NAVFAC P-307 contexts. The problem gives you a cylinder with a diameter of 4 feet and a height of 5 feet. The unit weight is 165 pounds per cubic foot. The task: figure out the weight of the solid aluminum cylinder.

First, a quick orientation: weight comes from volume times density (or unit weight, in this case). You measure how much space the object takes up, then you multiply by how heavy that space is per unit of volume. It’s a simple chain, but if any link is off, the result doesn’t quite sit right. So we start with the geometry.

Step 1: turn diameter into radius

• The diameter is 4 feet, so the radius r is half of that: r = 4/2 = 2 feet.

• Easy math, but crucial. In circular objects, radii drive the area, and area is the key to volume.

Step 2: calculate the volume

• The volume V for a solid cylinder is V = π r^2 h, where h is the height.

• With r = 2 ft and h = 5 ft, plug in:

V = π (2)^2 (5) = π (4)(5) = 20π cubic feet.

• π is about 3.14159. If you’re doing a quick numeric, V ≈ 20 × 3.14 = 62.8 cubic feet.

• So the cylinder holds about 62.8 cubic feet of space.

Step 3: multiply by unit weight to get the weight

• The unit weight is 165 pounds per cubic foot. Multiply by the volume:

Weight ≈ 62.8 ft^3 × 165 lb/ft^3.

• Do the arithmetic: 62.8 × 165 = 10,362 pounds.

• If you like a quick sense-check: round a bit—62.8 rounds to ~63 cubic feet; 63 × 165 ≈ 10,395 pounds. The precise figure from the problem setup lands at 10,362 pounds, which matches the standard answer for this combination of dimensions and unit weight.

Final answer: 10,362 pounds.

Why this tiny calculation matters in the real world

Engineers in naval and marine settings juggle weight like a chef juggles ingredients. A single solid aluminum cylinder might be a ballast piece, a structural stub, or a test component. Knowing its exact weight helps you:

• Balance ships or platforms so that stability and maneuverability aren’t compromised.

• Size fasteners, brackets, and supports that can handle the load without overbuilding.

• Plan for buoyancy and trim, especially when you’re assembling modular units or retrofit parts.

• Validate material specs and procurement estimates so you’re not buying too much or too little metal.

A quick note on unit weight and density

What you see here is a nice, clean example of unit weight, which is essentially density expressed as weight per unit volume. In metric terms, density is mass per volume; in imperial terms, unit weight is weight per volume. The unit weight you’re given (165 lb/ft^3) is material-specific. Aluminum isn’t a single fixed number—historically, it varies with alloy and temper—but for this problem, 165 lb/ft^3 is the value you use. That’s the number that converts your space into a meaningful weight.

Where people trip over this stuff (and how to avoid it)

• Radius vs. diameter mix-ups: always convert diameter to radius before squaring it in the volume formula. It’s the most common slip.

• Units, units, units: keep track of cubic feet when you’re multiplying by pounds per cubic foot. If you end up with inches or meters, you’ll need conversions. A tiny mismatch can throw off a heavy calculation.

• Pi and rounding: you don’t have to fib about π—use a standard value (3.14 or 22/7) for quick work, but keep track of how many decimals you’re using. The final answer will be sensitive if you’re dealing with big volumes.

• Real-world checks: does the result feel reasonable? If you calculate a massive weight for a small object, slow down and re-check the radius and height. A hands-on sanity check is your best friend.

A little more context where math meets design

In naval settings, every weight decision feeds into stability, load paths, and even safety margins. Engineers often pair this kind calculation with structural analyses, buoyancy assessments, and, yes, sometimes some rough thermal and corrosion considerations (aluminum’s corrosion resistance and fatigue behavior can affect long-term weight if components degrade). The math doesn’t exist in isolation; it’s the backbone of a bigger engineering conversation about how a vessel or facility behaves under real-world conditions.

A few tangents worth keeping in mind

• When a cylinder isn’t solid, the problem gets a tad more interesting. If you’ve got a hollow cylinder (a tube), you’d subtract the inner volume from the outer volume before applying the unit weight. The same formula applies, but the math changes with the geometry.

• Weight vs. mass: in everyday shipyard talk, people often say “weight” when they mean force due to gravity. If you’re working in a different system or altitude where gravity isn’t standard, you’ll see mass and weight distinguished. For practical shipyard calculations on Earth, using weight in pounds is perfectly fine.

• Material choices: aluminum is light for its strength, which is why it’s used widely in marine applications. Compared to steel, aluminum adds less deadweight, but you still need to account for its properties in the overall design.

Practical takeaways you can carry forward

• Start with the core formula: V = π r^2 h. If you have diameter instead of radius, convert immediately (r = d/2).

• Multiply the result by the material’s unit weight to get weight. Simple yet powerful.

• Keep a mental checklist: confirm r, confirm h, confirm unit weight, confirm math. It’s a tiny ritual that saves big headaches later.

• Use this pattern for similar problems: a cylinder, a cone, a rectangular prism—each shape has a clean volume formula, and once you’ve got the volume, the weight comes from the unit weight.

A final thought

The math behind a weight calculation isn’t just about plugging numbers into formulas. It’s about understanding how space, mass, and force come together in the real world. In naval engineering and related fields, this kind of thinking keeps projects on track, parts properly sized, and crews safe. So the next time you see a circle with a height attached to it, you’ll know there’s a neat, reliable way to turn dimensions into something tangible—like a precise weight that informs design and ensures everything sits correctly in its place.

If you ever stumble on a similar problem, you’ll have a simple roadmap: derive the radius from the diameter, calculate the volume with the cylinder formula, and multiply by the given unit weight. The numbers line up, the answer becomes clear, and you gain one more practical tool in your engineering toolkit. In a field where accuracy counts, that’s worth doing with care—and a touch of curiosity.