Mastering the Canadian Forces Aptitude Test: Surface Area Concepts

Getting ready for the Canadian Forces Aptitude Test (CFAT) can feel a bit like preparing for battle, right? Whether you're just starting your studies or finding yourself knee-deep in practice questions, understanding core math concepts—especially surface area calculations—is crucial. So, let’s break down a specific problem to guide you through it.

Imagine you have a rectangular box with dimensions of 3 cm wide, 2 cm deep, and 4 cm high. Not exactly a massive shipping container, but it's a great place to start our math adventure! To figure out the total surface area of this box, you’ll use the formula:

[ S = 2(lw + lh + wh) ]

Now, let’s plug those numbers in. If we set:

• (l) to the height (4 cm),
• (w) to the width (3 cm), and
• (h) to the depth (2 cm),

here’s what you do next:

1. Calculate (lw): ( 4 \times 3 = 12 )
2. Calculate (lh): ( 4 \times 2 = 8 )
3. Calculate (wh): ( 3 \times 2 = 6 )

Now, add these results together: [ S = 2(12 + 8 + 6) = 2(26) = 52 , \text{cm}² ]

There you have it—the surface area of the original box is 52 cm². But what happens if you double the dimensions? It’s like getting a surprise upgrade!

Double the width: (3 \times 2 = 6 , \text{cm})
Double the depth: (2 \times 2 = 4 , \text{cm})
Double the height: (4 \times 2 = 8 , \text{cm})

With these new dimensions, the calculations change a bit. Let’s now find the surface area of the new, larger box using the same formula:

1. Calculate (lw): ( 8 \times 6 = 48 )
2. Calculate (lh): ( 8 \times 4 = 32 )
3. Calculate (wh): ( 6 \times 4 = 24 )

Now, summing these results: [ S = 2(48 + 32 + 24) = 2(104) = 208 , \text{cm}² ]

And voilà! The total surface area of the box with doubled dimensions is 208 cm².

This problem demonstrates not just calculations, but also how math can provide insight into real-world scenarios, like packing for a big move or designing a packing box. Plus, it’s a foundational skill for your CFAT prep.

Remember, math is all about practice. The more you familiarize yourself with problems like these, the more confident you'll be. So grab some practice questions, hit the books, and make this material stick! You got this, and the CFAT success is right around the corner.