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30 Oct 2018, 02:50
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
28% (01:59) correct
72%
(02:38)
wrong
based on 69
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A single slice cut from the center of a circular pizza has an edge length (from the center of the pizza to the edge of the crust) of 5″, has an arc length of 1.25π″, and weighs 4 ounces. If a serving weighs 8 ounces, then, to the nearest integer, what is the largest number of servings that six 6″ diameter pizzas can yield? (Note that servings must weigh 8 ounces, but they do not need to be equal in shape.)
A. 1
B. 4
C. 6
D. 8
E. 9
A. 1
B. 4
C. 6
D. 8
E. 9
30 Oct 2018, 21:13
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Bunuel
The Timer shows all 5 wrong so the solution is here
We have to find the weight per unit of area
So radius =5, circumference =2*π*5=10π
The circumference is 1.25π or \(\frac{10π}{1.25π}\)=8th part of entire pizza, so the area of slice will be 1/8 of that of pizza= \(\frac{π*5^2}{8}\)=\(\frac{25π}{8}\) but this is 4 ounce, so double of it or 25π/4 will give 8ounces
Now area of 6 pizzas with radius 3=\(6*π*3^2=54π\)
Number of slices of 8ounces =\(\frac{54π}{\frac{25π}{4}}=\frac{4*54}{25}\)=4*2.16=8.64
Therefore 8 slices
D
05 Dec 2020, 18:02
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Bunuel
Solution:
Let’s determine the area of the slice of pizza that weighs 4 ounces. Since the radius of the slice is 5 inches and the arc length is 1.25π inches, the angle of the slice (measuring at the tip) is 1.25π/10π x 360 = 1/8 x 360 = 45 degrees. That is, a 45-degree slice of a pizza that has a radius of 5 inches (or a diameter of 10 inches) weighs 4 ounces. Now, let’s determine its area:
45/360 x 5^2 x π = 1/8 x 25π = 25π/8 sq. in.
That is, if a pizza (or portion of it) has an area of 25π/8 sq. in., it weighs 4 ounces. In other words, a pizza (or portion of it) having an area of 25π/8 x 2 = 25π/4 sq. in. would weigh 8 ounces (or 1 serving).
Now let’s determine the area of a 6-inch diameter (or 3-inch radius) pizza:
3^2 x π = 9π sq. in.
Thus, the combined area of six such pizzas is 6 x 9π = 54π sq. in. Dividing 54π by 25π/4, we have:
(54π) / (25π/4) = 54 / (25/4) = 54 x 4/25 = 216/25 = 8.64
Thus, at most 8 servings can be obtained from the pizzas.
Answer: D
