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7th Grade Math / Lesson 7: Finding Surface Area and Volume

SURFACE AREA AND VOLUME
What will we be learning in this lesson?


  • In this lesson you will look at the surface areas and volumes of different objects.
Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


SURFACE AREA AND VOLUME


  • The surface area of an object is the amount of area on the surface of each side of the object. If an object has six sides, you must find the area of each of those sides and add them all together to get the surface area of the object. If the object has 5 sides, find the areas of each of those 5 sides and add them together.

  • Reminder on finding areas of different shapes.

    Squares/rectangles: base * height

    Triangles:   ½ *base*height

    Circles: p * radius 2


SURFACE AREA AND VOLUME


  • The volume of an object is the amount of space inside of the object. If you had to fill the inside of an object with something, you would be dealing with the volume of the object.

  • Reminder on finding volumes of different objects.

    Squares/rectangles: base * height * width

    Prism: Area of the base * height

    Pyramid: 1/3 * area of the base * height


SURFACE AREA AND VOLUME


  • Use the dimensions of the object to find the surface areaand the volume.


  • First the surface area. Look at all of the sides and decide what shape they are. Find the areas of each of these shapes. This object has 5 sides. Two of them are triangles and 3 of them are rectangles.


SURFACE AREA AND VOLUME



  • If we start with thetriangles:   ½ * base * height
                                                      ½* 4 * 3 =   ½ * 12 = 6 sq cm
  • There are two triangles so we have two areas of 6 sq cm

  • Now the rectangle that is on the bottom. The dimensions are 4cm by 2 cm. The area of this rectangle is 4 * 2 = 8 sq cm

  • The rectangle on the side has dimensions 3 cm by 2 cm.
    The area of that one is 3 * 2 = 6 sq cm

  • The last rectangle is the one that is slanted. The dimensions of this one are 5 cm by 2 cm. The area is 5 * 2 = 10 sq cm


SURFACE AREA AND VOLUME


  • Now we just need to take all of the individual areas and add them together to get the total surface area of the object.

    Remember we had two triangles with an area of 6.      6 + 6 + 8 + 6 + 10=36

  • The surface area of this object is 36 sq cm

  • This is the amount of area on the surfaces of the object.


  • SURFACE AREA AND VOLUME


  • Now find the volume.

  • Decide what object this is. This is a prism. To find the volume of a prism, first find the area of the base (which is a triangle) then multiply this by the height (which could look like the depth).


  • SURFACE AREA AND VOLUME


  • The base is a triangle. The area of the base is found by   ½ * base * height of the triangle.
                                                                                                    ½ * 4 * 3 = 6
  • Now take this area and multiply by the height (depth) of the object.
    6 * 2 = 12

    The volume of the object is 12 cubic cm
    This is how much space there is inside of this object.


    • Can you find the surface area and volume of an object?
    • Go back to the classroom to get to your homework and any other items you need to attend to.