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# A single slice cut from the center of a circular pizza has an edge len

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Math Expert
Joined: 02 Sep 2009
Posts: 60646
A single slice cut from the center of a circular pizza has an edge len  [#permalink]

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30 Oct 2018, 02:50
00:00

Difficulty:

95% (hard)

Question Stats:

13% (03:38) correct 88% (02:40) wrong based on 22 sessions

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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

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Math Expert
Joined: 02 Aug 2009
Posts: 8336
A single slice cut from the center of a circular pizza has an edge len  [#permalink]

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30 Oct 2018, 21:13
Bunuel wrote:
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

The Timer shows all 5 wrong so the solution is here

We have to find the weight per unit of area

The circumference is 1.25π or $$10π/1.25π$$=8th part of entire pizza, so the area of slice will be 1/8 of that of pizza= $$\frac{π*5^2}{8}$$=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 =$$54π/\frac{25π}{8}$$=$$\frac{4*54}{25}$$=4*2.16=8.64
Therefore 8 slices

D
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A single slice cut from the center of a circular pizza has an edge len   [#permalink] 30 Oct 2018, 21:13
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