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6.3: Area, Surface Area and Volume

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    Definition: Area

    The extent or measurement of a surface or piece of land. (2 dimensional)

    clipboard_e1f9e59c0bfd55a35b3e0050cbc56a894.png
    Figure 6.3.1: 2 dimensional land

    Definition: Surface Area

    The area of such an outer part or uppermost layer. (3 dimensional)

    clipboard_e217ba7f1fdd8a8ff4ec446c816ab28a7.png
    Figure 6.3.2: Surface area (3 dimensional)

    Definition: Volume

    The amount of space that a substance or object occupies, or that is enclosed within a container, especially when great. (3 dimensional)

    clipboard_e3bdbf51c1ed072118b10e16c5b99d4eb.png
    Figure 6.3.3: Amount of space occupied by an object (3 dimensional)

    Partner Activity 1

    1. Why is area “squared”? i.e. \(15 \text { cm}^{2}\)
    2. Why is volume “cubed”? i.e. \(40 \text { liters}^{3}\)

    Partner Activity 2

    Think inside the box and approximate the Shaded Area: (area of a square is base times height)

    clipboard_e975a5ad0b002498edc8d693c317e82b6.png
    Figure 6.3.4

    Partner Activity 3

    Think around the box (surface area) and approximate the Shaded Area: (How many sides are not seen in the picture, which must be included in the final answer?)

    clipboard_ec7c2931ea187adb9b605d63dbd5156f1.png
    Figure 6.3.5

    Partner Activity 4

    Think inside the box (volume) and approximate the Shaded Area: Volume is base time’s height times width.

    clipboard_eeb7aeed233c6e03ad813b401933200bb.png
    Figure 6.3.6

    Practice Problems

    1. Explain the difference between area, surface area, and volume.
    2. Estimate the area of the following shapes:
      1. clipboard_e235ab6fb437a4e5c2516dbc3e6bd8539.png
      2. clipboard_e88ba0a3782eeb60a8538b52fd8553b74.png
      3. clipboard_e55bd62716191c5da41baf53ec3f92c3b.png
    3. Find the Surface Area of the following shapes:
      1. clipboard_e94123dd42f8e2142a9d80e0b8dba41b6.png
      2. clipboard_e682bad1f6d7fd7c31e308433ecc0e23c.png
    4. Find the Volume of the following shapes:
      1. clipboard_ee4b82bc2cc574d6ce4e8336b7ebaf970.png
      2. clipboard_ebc2ab80ea8ff736ed96eb5affcb31162.png

    This page titled 6.3: Area, Surface Area and Volume is shared under a not declared license and was authored, remixed, and/or curated by Amy Lagusker.

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      1. area
      2. surface area
      3. volume