Answer:
A) 153.9 in² (nearest tenth)
B) 506.7 cm² (nearest tenth)
C) Los Angeles pizza
D) 1.4
Step-by-step explanation:
Part A
A pizza parlor in Los Angeles sells a pizza with a 14-inch diameter. Assuming the pizza is a circle, we can use the area formula for a circle to determine its area:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Area of a circle}}\\\\A=\pi r^2\\\\\textsf{where:}\\\phantom{ww}\bullet\; \textsf{$A$ is the area.}\\ \phantom{ww}\bullet\;\textsf{$r$ is the radius.}\end{array}}[/tex]
The diameter of a circle is twice its radius. Given that the diameter of the pizza is 14 inches, its radius is r = 7 inches. Substitute r = 7 into the area formula and solve for A:
[tex]A_{L.A.}=\pi \cdot 7^2 \\\\ A_{L.A.}=49\pi \\\\A_{L.A.}=153.938040025... \\\\ A_{L.A.}=153.9\; \sf in^2\;(nearest\;tenth)[/tex]
Therefore, the pizza from Los Angeles is 153.9 square inches (rounded to the nearest tenth).
[tex]\dotfill[/tex]
Part B
A pizza parlor in London sells a pizza with a 25.4-centimeter diameter. The radius of a circle is half its diameter, so the radius (r) of the London pizza is:
[tex]r=\dfrac{25.4}{2}=12.7\; \sf cm[/tex]
To determine the area of the London pizza, substitute r = 12.7 into the area of a circle formula:
[tex]A_{\text{London}}=\pi \cdot 12.7^2 \\\\A_{\text{London}}=161.29\pi \\\\A_{\text{London}}=506.7074790974 ... \\\\A_{\text{London}}=506.7\; \sf cm^2\;(nearest\;tenth)\\\\[/tex]
Therefore, the pizza from London is 506.7 square centimeters (rounded to the nearest tenth).
[tex]\dotfill[/tex]
Part C
The pizza with the larger area has the larger diameter.
To determine which pizza has the larger area, we need to convert the diameter of the Los Angeles pizza into centimeters and then compare it with the diameter of the London pizza.
Given that 1 in = 2.54 cm, multiply the diameter of the Los Angeles pizza (14 in) by 2.54 to convert it to centimeters:
[tex]\textsf{Diameter of L.A. pizza}=14 \;\textsf{in} \cdot 2.54 \;\textsf{cm/in} \\\\ \textsf{Diameter of L.A. pizza}=35.56\; \sf cm[/tex]
As 35.56 cm is greater than 25.4 cm, the Los Angeles pizza has a larger diameter than the London pizza, and thus it has the larger area.
[tex]\dotfill[/tex]
Part D
To determine the scale factor relationship between the pizzas, divide the diameter of the Los Angeles pizza (in centimeters) by the diameter of the London pizza:
[tex]\textsf{Scale factor} = \dfrac{\textsf{Diameter of Los Angeles pizza}}{\textsf{Diameter of London pizza}}\\\\\\\textsf{Scale factor} = \dfrac{35.56\; \textsf{cm}}{25.4\; \textsf{cm}} \\\\\\\textsf{Scale factor} = 1.4[/tex]
Therefore, the diameter of the Los Angeles pizza is 1.4 times the diameter of the London pizza.
