Question: 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?

1. 33%
2. 44%
3. 56%
4. 67%
5. 78%

“A pizzeria makes pizzas that are shaped as perfect circles''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT quant section enables the students to be active in mathematical calculations. The students must select valid answer choices by making proper and suitable calculations. The students must have a solid idea of mathematical calculations to solve GMAT Problem Solving questions. The GMAT Quant topic in the problem-solving part cites multiple calculative problems that must be solved with better skills of quantitative. The candidates can answer more questions from the book “501 GMAT Questions”.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that:

Given:

• A pizzeria makes pizzas in the shape of perfect circles.
• He measures the size of the pizza by the diameter of the pizza.

Find Out:

• The percentage of the surface area of a 16-inch pizza larger than a 12-inch pizza.

In the case of 16-inch pizza, radius = 8
As per the formula of the circle, the area of 16-inch pizza = π (radius)^2 = π* 8^2 = 64π

In the case of 12-inch pizza, radius = 6
As per the formula of the circle, the area of 12-inch pizza = π (radius)^2 = π* 6^2 =36π

Since the question states that 16-inch pizza is larger than a 12-inch pizza, the difference in surface area = (64π- 36π)/ 36π = 28π/36π =28/36 =7/9 =77.7777% approx. = 78%
The percentage of the surface area of a 16-inch pizza larger than a 12-inch pizza = 78%

Correct Answer: (E)

Approach Solution 2:

The problem statement suggests that:

Given:

• A pizzeria makes pizzas in the shape of perfect circles.
• He measures the dimension of the pizza by its diameter.

Find Out:

• The percentage of the surface area of a 16-inch pizza larger than a 12-inch pizza.

The formula of percent greater than indicates that:
(New - Old)/Old* 100) or (Change/Original* 100)

The radius (r) of the 16-inch pizza, radius = 8
Therefore, the area of the 16-inch pizza = πr^2 = 64π (as per the formula of the circle)

The radius (r) of the 12-inch pizza, radius = 6
Therefore, the area of the 12-inch pizza = πr^2 = 36π (as per the formula of the circle)

Hence, the percent area of a 16-inch pizza is larger than the area of a 12-inch pizza
= (64π-36π/36π * 100)
= (28π/36π* 100)
= (7/9 *100)
=77.7777% approx.
= 78%

Correct Answer: (E)

Approach Solution 3:

The problem statement suggests that:

Given:

• A pizzeria makes pizzas in the shape of perfect circles.
• He measures the dimension of the pizza by its diameter.

Find Out:

• The percentage of the surface area of a 16-inch pizza larger than a 12-inch pizza.

If the shape of the pizza changes by a certain percentage, then the multiplier for the change in percent is the scale factor i.e k.
Therefore, to find the percent change, it is required to find the scale factor.
The scale factor has an impact on the length of the object.
Therefore, Area will be the product of the length = length * length
Thus, we can say,
Change in the percentage of the increased area= (scale factor * scale factor) =k^2

Here length is equal to the radius of the circle, let the radius of the circle be r
Therefore, k= r2/r1 = 8/6 =4/3 (since the diameter of one pizza is 16 inches and another pizza is 12 inches)
Percent change in area of the circles= k^2 = (4/3)^2 = 16/9 = 1.7777 approx = 1.78 approx
Therefore, the new area is = (1.78 - 1) = .78 = 78 percent greater that the smaller area of te circle.

Correct Answer: (E)

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