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A single slice cut from the center of a circular pizza has a
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24 Nov 2020, 11:44
24 Nov 2020, 11:44
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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
Re: A single slice cut from the center of a circular pizza has a
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25 Nov 2020, 00:17
25 Nov 2020, 00:17
1
Sample pizza r=5; d=10; c=10π; thus a single serving is 1/4th of this (c/1.25π=1/2 serving; 1/4*c=1 serving)
area of single serving=(r^2π)/4=25π/4=6.25π
Area of the six 6 inch diameter pizzas=6/2=r=3; 3^2π*6=54π; 54π/6.25π=8.64
Thus, it can serve 8 full servings. It could be argued that this, rounded to the nearest number is 9, which I regard as kinda unfair because that seems a very reasonable interpretation, but that's the value of reading the question, and it's somewhat reinforced by saying that servings "must weight" 8 ounces.
Ways to get tripped up:
-Not recognize that the reference pizza and the "new" pizzas are different
-Not recognize that the "new" pizzas have a diameter of 6, not a radius, as was given in the reference
-Miss the point about what constitutes a serving
area of single serving=(r^2π)/4=25π/4=6.25π
Area of the six 6 inch diameter pizzas=6/2=r=3; 3^2π*6=54π; 54π/6.25π=8.64
Thus, it can serve 8 full servings. It could be argued that this, rounded to the nearest number is 9, which I regard as kinda unfair because that seems a very reasonable interpretation, but that's the value of reading the question, and it's somewhat reinforced by saying that servings "must weight" 8 ounces.
Ways to get tripped up:
-Not recognize that the reference pizza and the "new" pizzas are different
-Not recognize that the "new" pizzas have a diameter of 6, not a radius, as was given in the reference
-Miss the point about what constitutes a serving
A single slice cut from the center of a circular pizza has a
[#permalink]
21 Jan 2021, 06:55
21 Jan 2021, 06:55
1
DFXR
Hi
I am not able to get the idea behind this
Area of the six 6 inch diameter pizzas=6/2=r=3; 3^2π*6=54π; 54π/6.25π=8.64
D = 6, r= 3, so area must be Pi r*r. so Pi*3*3 = 9 pi . why is it again multiplied by 6 and is 54pi?
pls help.
Hi
I am not able to get the idea behind this
Area of the six 6 inch diameter pizzas=6/2=r=3; 3^2π*6=54π; 54π/6.25π=8.64
D = 6, r= 3, so area must be Pi r*r. so Pi*3*3 = 9 pi . why is it again multiplied by 6 and is 54pi?
pls help.
