1. Volume & Surface Area

2. Objectives: Essential Question: Volume & Surface Area
Solve problems involving volume and surface area of cylinders, prisms, and composite shapes.
Essential Question:
How can I use what I know about area to calculate volume and surface area of cubes, prisms, and cylinders?

3. Volume & Surface Area
Cube: a 3D shape with six square or rectangular sides, a block.
Rectangular Prism: a polyhedron that has two parallel and congruent bases that are rectangles; a 3D solid with six rectangular faces.
Triangular Prism: a polyhedron that has two parallel, congruent bases that are triangles; a prism whose faces are triangles.
Cylinder: a 3D figure that has two parallel congruent bases.
Volume: the measure of space occupied by a solid region.
Surface Area: the sum of the areas of all the surfaces (faces) of a three dimensional figure.

4. Volume & Surface Area
Triangular Pyramid: a polyhedron with a three-sided polygon for a base and triangles for its sides; a pyramid with a triangular base.
Square Pyramid: a polyhedron with a four-sided polygon for a base and triangles for its sides; a pyramid with a square base.
Sphere: a perfectly rounded 3D object such as a ball.
Cone: a 3D figure with one circular base.

5. What is a 3D Figure: Volume & Surface Area What do they look like…
In previous years you have studied 2D shapes like squares, rectangles, parallelograms, triangles, circles, and trapezoids.
But now it is time to add a third dimension…

6. Volume & Surface Area
What is a 3D Figure:
What do they look like…

7. Some 3D Figures: Volume & Surface Area What do they look like… Cube
Rectangular Prism
Triangular Prism
Cylinder

8. Some Additional 3D Figures:
Volume & Surface Area
Some Additional 3D Figures:
What do they look like…
Triangular Pyramid
Square Pyramid
Sphere
Cone

9. Volume & Surface Area
Cubes:
What do they look like…

10. Volume & Surface Area
Prisms:
What do they look like…

11. Volume & Surface Area
Cylinders:
What do they look like…

12. A 3D shape with two parallel congruent polygon bases
Volume & Surface Area
3D Characteristics:
What makes what a what…
A 3D shape with two parallel
congruent polygon bases

13. 3D Characteristics: Volume & Surface Area What makes what a what…
A cylinder falls under its own category because
its bases are not considered polygons

14. 3D Characteristics: Volume & Surface Area What makes what a what…
Others include pyramids and cones because
they contain only one base. Their name is
derived based on the shape of the base

15. Important Volume Formulas:
Volume & Surface Area
Important Volume Formulas:
Rectangular Prism
Triangular Prism
Cube
Cylinder
V = s3
V = lwh
V = ½bhw
V = πr2h
V = bhw

16. Example 1: Cube Volume = s3 V = 3in x 3in x 3in V = 27in3
Volume & Surface Area
Example 1: Cube
Find the volume of the cube whose sides measure 3 inches.
Volume = s3
V = 3in x 3in x 3in
V = 27in3

17. Example 1: Rectangular Prism
Volume & Surface Area
Example 1: Rectangular Prism
Find the volume of the rectangular prism whose length is 5in, width is 9in, and height is 4in.
Volume = lwh
V = 5in x 9in x 4in
V = 180in3

18. Example 1: Triangular Prism
Volume & Surface Area
Example 1: Triangular Prism
Find the volume of the triangular prism whose length is 6cm, width is 4cm, and height is 3cm.
Volume = ½bhw
V = ½(6cm)(3cm)(4cm)
V = 36cm3

19. Example 1: Cylinder Volume = πr2h V = (3.14)(4ft)2(3ft) V = 150.72ft3
Volume & Surface Area
Example 1: Cylinder
Find the volume of the cylinder whose height is 3ft and radius is 4ft.
Volume = πr2h
V = (3.14)(4ft)2(3ft)
V = ft3

20. Example 1: Rectangular Prism
Volume & Surface Area
Example 1: Rectangular Prism
Find the volume of the rectangular prism.
V = lwh
V = 4in x 6in x 5in
V = 120in3

21. Example 1: Rectangular Prism
Volume & Surface Area
Example 1: Rectangular Prism
Find the volume of the rectangular prism.
V = lwh
V = 5in x 7in x 11in
V = 385in3

22. Example 1: Triangular Prism
Volume & Surface Area
Example 1: Triangular Prism
Find the volume of the triangular prism.
Volume = ½bhw
V = ½(15cm)(9cm)(4cm)
V = 270cm3

23. Example 1: Cylinder Volume = πr2h V = (3.14)(3cm)2(12cm) V ≈ 339.3cm3
Volume & Surface Area
Example 1: Cylinder
Find the volume of the cylinder.
Volume = πr2h
V = (3.14)(3cm)2(12cm)
V ≈ 339.3cm3

24. Independent Practice: Volume
Volume & Surface Area
Independent Practice: Volume
Find the volume of each 3d shape.

25. Independent Practice: Volume
Volume & Surface Area
Independent Practice: Volume
Answers.
m cm3
m mm3

26. Volume & Surface Area Find the volume of the block.
A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.
The block is a rectangular prism with a cylindrical hole. To find the volume of the block, subtract the volume of the cylinder from the volume of the prism.

27. Volume & Surface Area Find the volume of the block.
A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.
The volume of the box is about
72 – 9.42 = cubic centimeters.

28. Volume & Surface Area Answer Find the volume of the cube.
A moving company has boxes of various sizes for packing. The smallest box available has the dimensions shown below. Find the volume of a larger box that is 3 times as large.
12 in.
Answer

29. Volume & Surface Area Answer Find the volume of the cylinder.
A jumbo-size can of tomato soup is about 3 times the size of a standard-sized can of soup. The standard can has the dimensions shown. Find the surface area and volume of the jumbo-size can.
Answer

30. Formula Summary: Volume & Surface Area Rectangular Prism
Triangular Prism
Cube
Cylinder
V = s3
V = lwh
V = ½bhw
V = πr2h
V = bhw

31. When you think about the words
Volume & Surface Area
So What’s The Difference:
Now that we have studied volume it is time to move on to surface area…another important concept dealing with 3D shapes:
When you think about the words
SURFACE AREA
What comes to mind?

32. Surface Area & Nets: Volume & Surface Area
When thinking about surface area we need to be able to break down the 3D solid by its faces…for instance:
If took the above cube and cut along the edges we could open the solid and see that there a total of 6 squares (we call these faces) – the figure on the right is called a net

33. Surface Area & Nets: Volume & Surface Area
Each solid has its own set of faces or NET:

34. Important Surface Area Formulas:
Volume & Surface Area
Important Surface Area Formulas:
Rectangular Prism
Cube
SA = 6s2
SA = 2lw + 2lh + 2hw

35. Important Surface Area Formulas:
Volume & Surface Area
Important Surface Area Formulas:
Triangular Prism
Cylinder
SA = 2(½bh) + lw1 + lw2 + lw3
SA = 2πr2 + 2πrh

36. Example 1: Cube SA = 6s2 SA = 6(4in)2 SA = 6(16in2) SA = 96in2
Volume & Surface Area
Example 1: Cube
Find the surface area.
SA = 6s2
SA = 6(4in)2
SA = 6(16in2)
SA = 96in2

37. Example 1: Rectangular Prism
Volume & Surface Area
Example 1: Rectangular Prism
Find the surface area.
SA = 2lw + 2lh + 2wh
SA = 2(15)(9) + 2(15)(7) + 2(9)(7)
SA = 270mm mm mm2
SA = 606mm2

38. Example 1: Triangular Prism
Volume & Surface Area
Example 1: Triangular Prism
Find the surface area.
SA = 2(½bh) + lw1 + lw2 + lw3
SA = 2(½)(4.5)(3) + (6x3.75) + (6x3.75) + (6x4.5)
SA = 13.5in in in2 + 27in2
SA = 85.5in2

39. SA = 2(3.14)(3mm)2 + 2(3.14)(3mm)(8mm) SA = 56.52mm2 + 150.72mm2
Volume & Surface Area
Example 1: Cylinder
Find the surface area.
SA = 2πr2 + 2πrh
SA = 2(3.14)(3mm)2 + 2(3.14)(3mm)(8mm)
SA = 56.52mm mm2
SA = mm2

40. Volume & Surface Area Camping.
A family wants to reinforce the fabric of its tent with a waterproofing treatment. Find the surface area, including the floor, of the tent below.
Remember, a triangular prism consists of two congruent triangular faces and three rectangular faces.

41. Volume & Surface Area Camping. SA = 29 + 36.54 + 36.54 + 29 = 131.08
A family wants to reinforce the fabric of its tent with a waterproofing treatment. Find the surface area, including the floor, of the tent below.
bottom
left side
right side
two bases
SA = =

42. Volume & Surface Area
HOMEWORK