When studying the surface area of different shapes in Year 9 Math, it's important to know how to compare them.

What is Surface Area?

The surface area is the total space that the outside of a three-dimensional shape takes up. It helps us understand how big the outside of objects like cubes, prisms, and cylinders are.

How to Calculate Surface Area

To compare the surface area of different shapes, you first need to learn how to find it. Here’s how to do it for some common shapes:

1. Cubes:

   • To find the surface area of a cube, you can use this formula: $SA = 6a^2$
   • Here, $a$ is the length of one side.
   • For example, if $a = 3$, then: $SA = 6 \cdot 3^2 = 54 \text{ square units}$

2. Rectangular Prisms:

   • The formula for a rectangular prism is: $SA = 2(lb + lh + bh)$
   • Here, $l$ stands for length, $b$ for breadth, and $h$ for height.
   • If $l = 4$, $b = 3$, and $h = 2$, then: $SA = 2(4 \cdot 3 + 4 \cdot 2 + 3 \cdot 2) = 2(12 + 8 + 6) = 52 \text{ square units}$

3. Cylinders:

   • The surface area of a cylinder can be found using this formula: $SA = 2\pi r(h + r)$
   • In this case, $r$ is the radius and $h$ is the height.
   • If $r = 2$ and $h = 5$, then: $SA = 2\pi(2)(5 + 2) = 28\pi \text{ square units}$

Comparing Surface Areas

After you find the surface areas, you can easily compare them.

• For example:
  • If the cube has a surface area of 54 square units,
  • The rectangular prism has 52 square units,
  • And the cylinder has about $87.96$ square units (because $28\pi$ is about $87.96$).

Conclusion

In conclusion, by using formulas to calculate the surface areas of different shapes, you can compare their sizes. This skill is useful for understanding math better and can also help in real-life situations like packing, designing, and building!