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A pizzeria makes pizzas that are shaped as perfect circles, and measur

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A pizzeria makes pizzas that are shaped as perfect circles, and measur  [#permalink]

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New post 17 Apr 2018, 05:24
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A pizzeria makes pizzas that are shaped as perfect circles, and measures pizza size by the diameter of a pizza. By surface area, approximately what percent larger is a 16-inch pizza than a 12-inch pizza?

A. 33%
B. 44%
C. 56%
D. 67%
E. 78%

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Re: A pizzeria makes pizzas that are shaped as perfect circles, and measur  [#permalink]

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New post 17 Apr 2018, 05:33
Bunuel wrote:
A pizzeria makes pizzas that are shaped as perfect circles, and measures pizza size by the diameter of a pizza. By surface area, approximately what percent larger is a 16-inch pizza than a 12-inch pizza?

A. 33%
B. 44%
C. 56%
D. 67%
E. 78%


Area of 16-inch pizza = pi*8^2 = 64pi

Area of 12-inch- pizza = pi*6^2 = 36pi

16-inch pizza is larger than 12-inch pizza by (64pi-36pi)/36pi = 28pi/36pi = 28/36 = 7/9 = 77.7777% = Approximately 78%

Hence option E = 78% is the answer.
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A pizzeria makes pizzas that are shaped as perfect circles, and measur  [#permalink]

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New post 17 Apr 2018, 09:42
Bunuel wrote:
A pizzeria makes pizzas that are shaped as perfect circles, and measures pizza size by the diameter of a pizza. By surface area, approximately what percent larger is a 16-inch pizza than a 12-inch pizza?

A. 33%
B. 44%
C. 56%
D. 67%
E. 78%

Percent greater than formula

Percent greater than:
\((\frac{New-Old}{Old}*100)\) OR \((\frac{Change}{Original}*100)\)

The 16-inch pizza has \(r=8\) and
Area of \(\pi r^2=64\pi\)

The 12-inch pizza has \(r=6\) and
Area \(=\pi r^2=36\pi\)


Area of 16-inch pizza is what percent larger than area of 12-inch pizza?

\((\frac{64\pi - 36\pi}{36\pi}*100)=(\frac{28\pi}{36\pi}*100)=\)

\((\frac{7}{9}*100)\approx{.777}*100 \approx{78}\)
percent

Answer E

Scale factor, k, squared - Typically quicker

If a geometric shape changes by a certain percent or fraction, the multiplier for the percent change is the scale factor, \(k\)

If you find scale factor, you find percent change

Scale factor affects length.
Area = length * length, so
"Percent change" of an increased area =
(scale factor*scale factor) = \(k^2\)

Length = radius = \(r\)
\(k=\frac{r_{2}}{r_{1}}= \frac{8}{6}=\frac{4}{3}\)

Percent change in area here = \(k^2= (\frac{4}{3})^2=\frac{16}{9}\approx{1.7777}\approx{1.78}\)

New area is
\((1.78-1)=.78=78\) percent greater than smaller area

Answer E
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Re: A pizzeria makes pizzas that are shaped as perfect circles, and measur  [#permalink]

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New post 19 Apr 2018, 16:52
Bunuel wrote:
A pizzeria makes pizzas that are shaped as perfect circles, and measures pizza size by the diameter of a pizza. By surface area, approximately what percent larger is a 16-inch pizza than a 12-inch pizza?

A. 33%
B. 44%
C. 56%
D. 67%
E. 78%


A 16-inch pizza has a surface area of π x 8^2 = 64π.

A 12-inch pizza has a surface area of π x 6^2 = 36π.

Now we can determine what percent larger the 16-inch pizza is versus the 12-inch pizza.

(64π - 36π)/36π x 100 = 28/36 x 100 = 7/9 x 100 ≈ 78%.

Answer: E
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Re: A pizzeria makes pizzas that are shaped as perfect circles, and measur &nbs [#permalink] 19 Apr 2018, 16:52
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