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2D and 3D Area, Volume and Surface Area

7.G.B.6
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Aligned To Common Core Standard:

Grade 7 Geometry - 7.G.B.6

What is 2D and 3D Area, Volume and Surface Area? 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 breadth; 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. 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. Surface area - Is the size of 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 it's 6 sides.

Printable Worksheets And Lessons




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 in2 . 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?



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." The surface area of the 3D object is calculated 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!