General question about finding the area of a circle.

[jtbeans]

Hello,

I've been brushing up on my math and came across this question:

Which of the following collections of round pizzas has the largest area?

One 21in pizza
Two 15in pizzas
Three 12in pizzas
Four 9in pizzas


I couldn't remember the formula for finding the area of a circle so I looked it up. This is what I found:
Area of a circle = pi r ²


What confuses me is that the question doesn't actually state what the measurement of the pizza pie is, which is frustrating, but assuming it's the radius... I'm concerned by the answer I get from my calculator (it seems too high):
A = pi ( 21 * 21 )
1385.44236023

That seems awfully high... not only that, but the website I got the question from left pi out of the equation all together, below is a copy of their solution, but is it even correct?

The area is proportional to the squared radius and the number of pizzas.
2 x 15² = 2 x 225 = 450
21² = 441
3 x 12² = 3 x 144 = 432
5 x 9² = 5 x 81 = 405 ​

 

[wjm11]

Hello,

I've been brushing up on my math and came across this question:

Which of the following collections of round pizzas has the largest area?

One 21in pizza
Two 15in pizzas
Three 12in pizzas
Four 9in pizzas


I couldn't remember the formula for finding the area of a circle so I looked it up. This is what I found:
Area of a circle = pi r ²


What confuses me is that the question doesn't actually state what the measurement of the pizza pie is, which is frustrating, but assuming it's the radius... I'm concerned by the answer I get from my calculator (it seems too high):
A = pi ( 21 * 21 )
1385.44236023

That seems awfully high... not only that, but the website I got the question from left pi out of the equation all together, below is a copy of their solution, but is it even correct?

The area is proportional to the squared radius and the number of pizzas.
2 x 15² = 2 x 225 = 450
21² = 441
3 x 12² = 3 x 144 = 432
5 x 9² = 5 x 81 = 405 ​

Pizza sizes given are diameters. Use half of that for radius.

 

[jtbeans]

Thanks guys, but I'm not sure I'm getting what I need out of this place yet as I still have many questions unanswered.

Pizza sizes given are diameters. Use half of that for radius.

How was I supposed to know that? Do people honestly get graded by testing in this way? I have never known that "all" pizzas come measured in Diameter - or that I was somehow supposed to assume it was diameter. Why? Because I've seen it both ways in real pizzerias.

On a closed-book test this questions lack of background info is stupefying.

You're not asked to calculate the areas, but to find the largest.

They only provide one measurement for each pizza, which can only be assumed as the diameter (or radius) so the only thing I have to calculate is Area... So I don't see how the "size" is supposed to be any different than the "area" of the pie - especially since the "size" (whatever that is) is so much smaller.

What I'd really like to know: How the Area is so large for a 21" pizza (1385.44236023). Am I doing something wrong with my original calculation?

 

[Ishuda]

...They only provide one measurement for each pizza, which can only be assumed as the diameter (or radius) so the only thing I have to calculate is Area... So I don't see how the "size" is supposed to be any different than the "area" of the pie - especially since the "size" (whatever that is) is so much smaller.

As mentioned earlier, it really doesn't matter whether it is the radius or the diameter. Suppose it were the radius, then the areas would be as you figured and you would have your largest area answer. But suppose it were the diameter (or twice the diameter or one tenth the diameter or ... just to be ridiculous), then you would have to multiply each of your computations by the same constant (1/4 in the case of the diameter) and so the largest of your computations would still give the correct answer.

What I'd really like to know:How the Area is so large for a 21" pizza (1385.44236023). Am I doing something wrong with my original calculation?

Well, as mentioned earlier, the sizes are generally a diameter and, because of the size, probably the 21" is in this case. If that is the case, you need to divide that number by 4 and a pizza of about 346 in² is 'more reasonable'. However, if it really were a 21" radius (about 3.5 ft in diameter), then the ~1385 in² would be correct.