Math 7 B: Surface Area Unit test Unit 6 Lesson 11

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It seems you are looking for help with a Math 7 unit test on surface area. While I cannot provide specific test questions or answers, I can review key concepts related to calculating surface area and help explain them. Here are some important points and formulas that you may find useful:

Surface Area of Common Geometric Shapes

  1. Rectangular Prism:

    • Formula: \( SA = 2lw + 2lh + 2wh \)
    • Where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
  2. Cube:

    • Formula: \( SA = 6s^2 \)
    • Where \( s \) is the length of one side.
  3. Cylinder:

    • Formula: \( SA = 2\pi r(h + r) \)
    • Where \( r \) is the radius and \( h \) is the height.
  4. Sphere:

    • Formula: \( SA = 4\pi r^2 \)
    • Where \( r \) is the radius.
  5. Cone:

    • Formula: \( SA = \pi r(r + l) \)
    • Where \( r \) is the radius of the base and \( l \) is the slant height.

Tips for Surface Area Problems

  • Always ensure your measurements are in the same unit before performing calculations.
  • Remember to calculate the area of each face separately if needed, and then sum them up.
  • For composite shapes, you may need to divide the shape into simpler shapes, calculate the surface area for each, and then add or subtract areas as necessary.

Example Problems:

  1. Rectangular Prism: What is the surface area of a rectangular prism with length = 5 cm, width = 3 cm, and height = 4 cm?

    • \( SA = 2(5)(3) + 2(5)(4) + 2(3)(4) = 30 + 40 + 24 = 94 , \text{cm}^2 \)
  2. Cylinder: Find the surface area of a cylinder with radius = 3 cm and height = 7 cm.

    • \( SA = 2\pi(3)(7 + 3) = 2\pi(3)(10) = 60\pi , \text{cm}^2 \approx 188.4 , \text{cm}^2 \)

If you have specific types of problems or formulas you'd like clarified or if there are particular concepts you're struggling with, feel free to ask!