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Surface area is the total area of the surface of an object. It applies to three-dimensional shapes. Understanding this value is critical in medicine as we try to develop and learn new methods for combating bacteria and viruses. If we can calculate the total area of the surface these organisms we can often give the proper dose of medication that in too high concentrations will be toxic to the cell.

What does surface area tell you about an object? Mathematics surely seems like a very boring and complicated subject, but there are lots of interesting things that the subject holds in itself. Counting, geometry, fraction… So many things! First, let us understand what it stands for. In very simple words, the surface area of an object is the total measure of the area that the object occupies. For example, if you draw a square on a piece of paper, the amount of space it takes on the page will be this measure. For each shape we study, we have a specific formula to calculate the surface area. And it is pretty easy to calculate too. All you have to do is add the measure of all the sides of the shape, and you will be able to use a formula to decipher it. These worksheets explain how to calculate the surface area and volume of different geometrical solids (cylinders and pyramids). When you are trying to calculate the final answer you need to take into account the shape of the object you are studying.

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Surface Area Worksheets

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Solids and Cylinders Lesson

This worksheet explains how to break down the surface area and volume of a standard cylinder using a series of formulas. A sample problem is solved, and two practice problems are provided.

Worksheet

Students will calculate the surface area and volume of different geometrical solids using the ten problems that are provided.

Practice

Much of the same type of problems that we have been working on and getting in the right frame of mind with.

Review and Practice

The concept of how to calculate the surface area and volume is gone over in a sample exercise that is completed for you and then you get a go at six of your own problems.

Quiz

Students will demonstrate their proficiency with this skill. Ten problems are provided.

Concept Check

A great worksheet to see where your student are with calculating surface area and volume. Three problems are provided, and space is included for students to copy the correct answer when given.

Surface and Volume of Cubes - Meet the Skill

Find the volume (v) for given cube. A cube is a region of space formed by six identical square faces joined along their edges. Three edges join at each corner to form a vertex.

Try the Skill

The surface area of one square is L x L = L². Just to remind you how these formulas flow.

Practice the Skill

Find the volume (V) for each cube when you are given all their needed measures.

Practice the Skill Twice

Put it all together and solve up those cubes much in the same way we completed the previous worksheet.

Show the Skill

Find the surface area (SA) or Volume (V) for each cube. You have eight to solve in this activity.

Warm Up

Find the two measures of interest for each cube that you are running with.

Rectangular Solids - Meet the Skill

This lesson walk you through working this skill on one of favorite shapes. A rectangular solid is a 3 dimensional object with six sides, all of which are rectangles. A solid figure, that has two pairs of parallel opposite faces and congruent bases are all rectangles.

Try the Skill

We spend a good bit of time with these two formulas: Surface Area of a rectangular solid = 2(lh) + 2(lw) + 2(wh). Volume of a rectangular solid = l x h x w. Here, l = length, h = height and w =width.

Practice the Skill

Even it may be hard to tell, these are all the same geometric shape. It does not matter how much we turn and twist them, they are still the shape figure.

Practice the Skill Twice

More of the same with this series of exercises to work through.

Show the Skill

More work for you on this one. The more opportunities you get to work on it, the better.

Warm Up

Use those formulas and see where it gets you with this concept.

Meet the Skill

It may not look like it, but the given figure is a cylinder. It can be seen that it is made up of 2 circles and one curved surface which when opened flat, is a rectangle.

Packed Squares - Try the Skill

A cube is nothing but a six squares packed together to form one solid figure. This means if area of one square is side² then area of cube will be 6 side².

Practice the Skill Twice

Find the surface area of an isosceles triangular prism with equal sides of triangle being 15 cm, base is 5 cm and its height is 11 cm and side is 12 cm.

Show the Skill

Find the total surface area of the given real world objects. Example: Suppose a water tank in the shape of a right circular cylinder is 30 ft long and 8 ft in diameter. How much sheet metal was used in its construction?

SA Warm Up

A cube has a side of 5 ft 7 in. Find the surface area of the cube. Suppose there is another cube whose side is 187% of the side of the above given cube. What percentage is the surface area of the smaller cube of the SA of the bigger cube?

SA of a Rectangular Prism - Meet the Skill

This figure is a type of solid identified as cube, it is a space figure as it is not two dimensional hence not flat and reside in space. These figures have faces, vertex, and edges. Faces are flat sides with area, Edge is a line segment where two faces meet and vertex is a corner where three or more edges meet.

Try the Skill

Most of the solid figures like the cube has a flat figure called a net which when folded together gives its respective solid shape. So if both the nets given above are cut out and folded then we can find out which figure folds up to make the required shape.

Practice the Skill

The edge of a cube is 2 ft. What will be its surface area?

Practice the Skill Twice

You will work on this problem in reverse. The surface area of cube is 64 square inches. What is the area of one of its faces?

Show the Skill

Which of the following patterns can be folded to make a cube?

Warm Up

The surface area of cube is 729 square centimeters. What is the area of one of its face? What is its volume?

Rectangular Prism Warm Up

Really fun thinking problems like: Can this pattern be folded to form a cube?

Determining SA and Volume of Rectangular Solids- Worksheet 1

Volume of Rectangular solid = Length x Breadth x Height Determine the area and perimeter and Volume of the Rectangle.

Worksheet 2

Determine the area and perimeter of the triangles, parallelograms, and trapezoids.

Review

Determine the surface area and volume of a series of rectangular solids.

Self Check

Volume of a rectangular solid = Length x Breadth x Height. SA = 2 x (Area of side 1 + Area of side 2 + Area of side 3).

Practice SA and Volume

Six rectangular shapes for you to work with.

Quiz

Find that answer ten more times using the skills that you have learned here.

Do Now

This is meant to be completed as an entire class. Complete the problems. Put your answer in the "My Answer" box.

Solids and Cylinders - Meet the Skill

Using the formula Volume = (base x height x length)/2 By using this formula, we will get the volume of triangular solid.

Try the Skill

Using the formula Area of cylinder = Area of two circle + Area of curved portion Area of cylinder = 2pr² + 2prh

Practice the Skill

Find the surface area of solids and cylinders.

Practice the Skill Twice

Fill in those shapes boss and while you are at it, find a few measures about them.

Show the Skill

My end all be all worksheet that tests where you are top to bottom with this series of skills and concepts, for that matter.

Warm Up

Find the surface area of the following figure. We also spend some time on volume too.