12. find the surface area of each figure to the nearest tenth.
a. show your work
b. what is a real-world example or use of surface area?

  12a. 471.2 cm²

  12b. 60 m²

Step-by-step explanation:

Part A.

The surface area of each figure is the sum of the end area and the lateral area.

  cylinder

  S = (2)(πr²) +2πrh = 2πr(r +h)

  S = 2π(5 cm)(5 cm +10 cm) =150π cm² ≈ 471.2 cm²

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  triangular prism

  S = (2)(1/2)bh + PL . . . . b=triangle base; h=triangle height; P=triangle perimeter; L=length of prism

  S = (4 m)(1.5 m) + ((4 + 2·2.5) m)(6 m) = (6 + 54) m² = 60 m²

Part B.

Surface area is useful in the real world wherever products are made from sheets of material or wherever coverings are applied.

Carpeting or other flooring, paint, wallpaper are all priced in terms of the area they cover, for example.

The amount of material used to make containers in the shapes shown will depend on the area of these containers (and any material required for seams).

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.