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At a certain pizza parlor, the diameter of a large pizza is [#permalink]
10 Oct 2012, 10:04

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Difficulty:

35% (medium)

Question Stats:

67% (09:27) correct
33% (01:03) wrong based on 183 sessions

At a certain pizza parlor, the diameter of a large pizza is 40% larger than the diameter of a small pizza. What is the percent increase in total amount of pizza, from a small to a large?

Re: At a certain pizza parlor, the diameter [#permalink]
10 Oct 2012, 10:18

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Let the pizzas be thin crust! Not considering height.

Small : diameter x, radius x/2, area (total amount of pizza) = pi * (x/2)^2 Large : diameter 1.4x, radius 1.4x/2, area (total amount of pizza) = pi * (1.4x/2)^2 = (1.4)^2 * area of small pizza = 1.96 * area of small pizza

Re: At a certain pizza parlor, the diameter [#permalink]
10 Oct 2012, 10:38

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mikemcgarry wrote:

At a certain pizza parlor, the diameter of a large pizza is 40% larger than the diameter of a small pizza. What is the percent increase in total amount of pizza, from a small to a large? (A) 20% (B) 40% (C) 64% (D) 80% (E) 96%

We need to find by what percent is the area of big pizza greater than the area of small pizza.

Since D (diameter) in the area formula is squared (area=\frac{\pi*d^2}{4}), then 40% increase in diameter, or increase 1.4 times, would be equivalent to 1.4^2=1.96 times increase in the area, which is the same as 96% increase.

Re: At a certain pizza parlor, the diameter [#permalink]
23 Nov 2013, 01:01

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Re: At a certain pizza parlor, the diameter of a large pizza is [#permalink]
13 Dec 2013, 09:45

At a certain pizza parlor, the diameter of a large pizza is 40% larger than the diameter of a small pizza. What is the percent increase in total amount of pizza, from a small to a large?

If A = pi (r)^2 the A = pi (1/2d) ^2 Area (small) = pi (1/2d)^2 Area (small) = pi (1/4d)

Area (large) = pi (1/2*1.4d)^2 Area (large) = pi (1/2*7/5d)^2 Area (large) = pi (49/100d)

So, the radius of the large pizza is roughly 50% larger than the smaller pizza. If we plug in a number for d we can see the difference in sizes. Area (small) = pi (1/4d) Area (small) = pi (1/4 * 36) Area (small) = pi(9)

Area (large) = pi (49/100d) Area (large) = pi (49/100 * 36) Area (large) = pi(18)

Therefore the area of the larger pizza is approximately 100% greater.