Answer:
The minimum width of the placemat is 10 inches.
Step-by-step explanation:
Let suppose that placemat has a square form, whose width must be at least equal to the diameter of the pizza, so that pizza does not touch the table. Hence, the following relationship is obtained:
[tex]w = D[/tex]
Where:
[tex]w[/tex] - Width of the placemat, measured in inches.
[tex]D[/tex] - Diameter of pizza, measured in inches.
The area of the pizza, measured in square inches, is determined by this formula:
[tex]A = \frac{\pi}{4} \cdot D^{2}[/tex]
The diameter is cleared afterwards:
[tex]D = \sqrt{\frac{4\cdot A}{\pi} }[/tex]
If [tex]A = 78.5\,in^{2}[/tex] and [tex]\pi = 3.14[/tex], then:
[tex]D = \sqrt{\frac{4\cdot (78.5\,in^{2})}{3.14} }[/tex]
[tex]D = 10\,in[/tex]
The minimum width of the placemat is 10 inches.
The minimum width of a placemat that can be placed underneath the pizza so that the pizza wouldn't touch the table is; 10 inches
We are told that the pizza has an area of 78.5 in². Thus;
A = 78.5 in²
Now, the pizza is circular in shape and the minimum width of a placemat that can be placed underneath the pizza so that the pizza wouldn't touch the table will be the diameter of the pizza
Thus, area of a circle with diameter d is;
A = πd²/4
Plugging in the relevant values, we have;
78.5 = 3.14d²/4
d² = 78.5 × 4/3.14
d² = 100
d = √100
d = 10 inches.
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