# Surface Area Worksheets

Surface area is an escaping and often hard to quantify measure. The surface area of a solid object is a measure that is a play on words of the title it is the entire area of the surface of the object. Think about an orange, the citrus fruit. If you were to peel the orange and then flatten out all the orange rind by rolling it with a rolling pin, you could calculate this measure by finding the total area of all the rind. This is what makes this measure so unique, it takes place in a 3-dimensional world, and we are accustomed to measuring things in 2 dimensions. In this section we will examine these measures in many different objects. We will also explore the concept of volume and multi-dimensional space.

### Aligned Standard: Grade 7 Geometry - 7.G.B.6

- Wrapping Paper Step-by-step Lesson- If you are so worried about how much the wrapping paper costs, why even bother wrapping the gift?
- Guided Lesson - It's amazing the things you can figure out with just a few little measures.
- Guided Lesson Explanation - Some of these problems require a great number of steps. I tried my best to minimize the number of steps for you.
- Practice Worksheet - I threw a number of quality real world problems in this one.
- Matching Worksheet - Match the problem to their measures. I removed the units.
- Surface Area and Volume of Solids and Cylinders Five Worksheet Pack - Attack of the cylinders and cones. Yes, they are all open.
- Analyzing in 3D Five Worksheet Pack - There are some true/false questions on here that are not clear. I think a rewrite is in order.
- Volume and Surface Area of Solids and Cylinders Five Worksheet Pack - These are all presented in word problem format.
- Finding the SA and Volume of a Cube Five Worksheet Pack - Use the symbol next to each equals sign to be your guide.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Just about every problem I see at the National level revolves around wrapping a present.

- Homework 1 - Troy wrapped a box he had with wrapping paper for his friend’s birthday. The wrapping paper was two cents per square inch. How much will the paper cost for the box below?
- Homework 2 - Max needs to wrap a present for his friend, but he is not sure that he has enough money to buy the wrapping paper. The wrapping paper costs 6 cents per square inch. He has $24.00. How much change will Max receive if he pays for the wrapping paper with that bill?
- Homework 3 - Sally stores her gloves and hats in a locker. She wants to cover the box with sticker paper to make it look blue. The sticker paper costs 4¢ per square inch. How much will it cost to cover the locker in sticker paper?

### Practice Worksheets

We look at many different geometric shapes and start to understand their measurements.

- Practice 1 - Find the SA of the cylinder.
- Practice 2 - A triangle has an area of 24 square feet. The height is 6 feet. What is the length of the base?
- Practice 3 - The radius of cone is 10 in
^{2}. What is the SA and volume of the cone?

### Math Skill Quizzes

See how you do on the stacking problems. There is effort to make those a greater part of standard.

- Quiz 1 - We will take a look at cylinders and cones and go after their measures.
- Quiz 2 - Assuming that blocks need not sit on top of one another, what is the number of blocks in this stack?
- Quiz 3 - Assuming that blocks need not sit on top of one another, what is the minimum number of blocks in this stack?

### What Is 2D and 3D?

**2D Area** - Any shape that has two dimensions are known as 2D shapes. We see many 2D shapes around us, such as triangle, square, rectangle, and many more! When a shape is 2D, it has only two measurements, length, and width. The total surface size that is enclosed within the 2D shape is known as it's area. The measure is represented in square units, for example, square inches, square meters, or square centimeters.
**3D Area** - Any shape that has three dimensions is known as 3D shape. There are many 3D shapes, including prisms, cubes, cylinders, and a lot more. This measure in three-dimensional objects is referred to as "surface area." To determine this measure in a 3D object is done by getting the total sum of all of its sides. For example, for calculating the surface area of a cube, we will take the total of all its 6 sides. Just like the standard measure it is represented in square units, the SA is calculated in square foot.
If someone asks your age, you say "I'm 13 years old." Isn't that correct? You use "years old" to imply that you are thirteen years of age. Just like that, when we are talking about a large surface area, we denote it by saying "This flat is 700 square foot."
So what is square foot? Let's take a look at it.
Take your room for example. It covers up a large space in your house. The space it covers is known as surface area. Now when you are looking for this measure, you will calculate it in square foot.
Just like for measuring time use seconds or minutes, for surface area, the S.I unit is known as square foot.
We calculate the SA of various shapes such as triangles, squares, rectangles and many more!

### How Do You Determine the Surface Area of a 2D or 3D Figure?

**2D & 3D shapes** - There are numerous objects around us in different shapes and sizes. We can see circles, hexagons, triangles, rectangles, and squares everywhere. Some are simpler shapes having only length and width; they are called 2-D shapes and made of straight or curved lines. 2-D shapes can have any number of sides. Any figure that has a plane object with only length and breadth (2 dimensions) has a 2D area. 3D shapes, like balls and ice-cream cones, are examples of 3D shapes. These shapes have more depth in them and can be much more complex to unfold and understand.

There are many different measures about these shapes that can help you understand and eventually manipulate them for your own use, but none more so than the concept of surface area and volume.

**Surface area** - You can find this measure in any object by determining the space covering the total object. Because things in the real world have 3 dimensions, smaller things have a great deal of surface area. How do you calculate this measure in a 3-dimensional object? Breaking it down, it is the sum total of all the areas of a particular shape that cover the surface of the object. For example, the surface area of a cube is a calculation that considers all of its 6 sides. Since there are 6 sides the equation could be stated as: A = 6a^{2}.

**Volume** - There are many other measures that people will often confuse with surface area, none more so than volume. The volume of an object is the measure of how much space it takes up when placed in a specific region. For example, the volume of two shoeboxes would be twice when compared with a single box volume. Because they take up twice the amount of space. Every shape has a different volume and a unique formula depending on its structure.

Due to the uniqueness of these measures in the biological world they often use a surface area to volume ratio to explain the shape of cellular surfaces. This simple ratio can be used to gauge many physical and chemical properties of cell parts. This ratio tends to change within organisms as they mature or begin moving.