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Easy

Question


Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
Carrie redesigned the container because the initial sketch did not account for cushioning material between the glasses. The area of the base of the newly designed container is 25 straight percent sign  greater than the area of the base in the initial sketch. What is the area, in square inches, of the base of the newly designed container?

hintHint:

Hint:
We simply need to find the area of the new container where the area of the base is 25% greater than the previous design. First we find 25% of the area of the base of the previously designed container and then just add that value to the area of the previously designed container to find the area of the newly designed container.

The correct answer is: 135


    Initial length of the base of the container = 12 inches
    Initial breadth of the base of the container = 9 inches
    Thus, initial area of the base of the container = left parenthesis 12 cross times 9 right parenthesis square inches
    = 108 square inches
    According to the question, the new area of the base is 25% greater than the initial area of the base.
    First we find the increase in the area of the base
    25% of initial area is given by
    25 straight percent sign text  of  end text 108 equals 25 over 100 cross times 108 equals 27
    The increase in the area of the base is by 27 square inches
    Thus, the new area of the base = (108+27) square inches
    = 135 square inches
    = 135 square inches
    Thus, the area of the base of the newly designed container = 135 sq.inches

    Note:
    There is a shorter way of doing this problem. There is a simple rule followed while increasing or decreasing a value by a certain percentage.  When we decrease a quantity by x%, we multiply the quantity by (1-0.x). Whereas when we increase a quantity by x%, we multiply it with (1+0.x).

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