At a certain pizza parlor, the diameter of a large pizza is

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.

E




(A) 20%
(B) 40%
(C) 64%
(D) 80%
(E) 96%

Let small pizza diameter = 100

Large pizza diameter would be = 140

Area of Circle \(= \pi * (\frac{d}{2})^2\)

\(= \frac{\pi}{4} * d^2\)

In the above, only variable is the diameter

\(100^2 = 10000\)

\(140^2 = 19600\)

Difference = 9600 or 96%

Answer = E

We need the areas of the pizzas. We know: area (of circle)=r²*pi. 2r =d.

Now pick smart numbers:

diameter of small pizza: 10, then diameter of big pizza: 14

then: area small pizza: 25pi, area of big pizza = 49pi

Hence percent increase 49/25 = 1.96 = 96 % bigger.

\(40 + 40 + \frac{40*40}{100} = 96\), Answer will be (E)

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