Yummy Pizza

Geometry Level 2

A pizza shop sells two round pizzas which have same thickness but are different in size. The smaller one has a diameter of 30 cm. The larger one has a diameter of 60 cm and costs twice the price of the smaller one.

In terms of value for money, which of the following statements is true?

Note

  • Here we take value to mean price. I.e. which option gets you pizza at the lowest cost per unit area.
Source: PSA 2014.
The smaller pizza has better value. The larger pizza has better value. More information is needed to work out. Each pizza has equally good value.

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19 solutions

Rugved Dhore
Mar 22, 2014

As thickness is the same, the area will decide the quantity of pizzas. Hence by finding areas of both the area of larger is 4 times the smaller. hence larger pizza has greater cost.

larger pizza has 4 times the area and even at twice the cost its a better buy

Safal Mittal - 7 years, 2 months ago

I got this sum in PSA

Isaac Gini - 7 years, 2 months ago

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Same Pinch!!!

Arya Samanta - 7 years, 2 months ago

What is PSA?

Calvin Lin Staff - 7 years, 2 months ago

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PSA means problem solving assessment.

Gaurav singh - 7 years, 2 months ago

PSA is an examination held since 2013 in India by CBSE for class 9 ,10 and 12 . One need to pass this PSA to be eligible for board examination .

SAURAV KUMAR NISHANT - 7 years, 2 months ago

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@Saurav Kumar Nishant it is not a matter of passing the examination..the `Problem Solving Assessment’ marks will be counted towards FA-4 which is 10% of total assessments of the whole academic year..

Pallavi Bhat - 7 years, 2 months ago

PSA is a abbreviation for Problem Solving Assessment.

Rhishikesh Dongre - 7 years, 1 month ago

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@Rhishikesh Dongre Even I am a fan of vegeta ssj2.

Manish Maharaj - 5 years, 1 month ago

me too bro

Uttam Bhadauriya - 7 years, 2 months ago

volume of pizza received per unit cost will decide which of the two sizes has greater value for money. Now consider the following: 1. Volume of a uniform body= (area) .(thickness) 2. Thickness being the same for two pizzas, volume is dependent on area alone. 3. Pizza being circular, area=[(pi).(d.d)]/4, consider (pi)/4 as a constant, say k 4. So area = k.(d.d) 5. Area of smaller pizza = k.(30.30)= 900k------- (i) 6. Area of larger pizza = k.(60.60) = 3600k-------(ii) 7. We see (ii) is greater that twice of (i). But it costs only twice of (i). 8. That is , you are getting more than twice the area of smaller pizza at just twice its cost. So a bigger pizza is a better deal. Order that one :)

Kumar Ujjwal - 7 years, 2 months ago

What if the topping is less? :P

Sabeel Mahmood - 7 years, 2 months ago

sorry dude u r ans is wrong as area of smaller pizza is pi r^2 and larger is pi (2R)^2. so smaller pizza is costly and has more value

Adithya krishna - 7 years, 2 months ago

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see cost smaller is x then larger is 2x but area is smaller is A and larger is 4A

Adithya krishna - 7 years, 2 months ago

Although it has more value (as u say), meaning that it is "costly", but the question asks fr d pizza which is "value for money" which means that "which would be better to buy"or "more volume in proportion to the price". So, the larger pizza though costs twice, but it offers much more volume of pizza, so that's obviously a better buy, meaning that it has "more value for money"! It's just that u didnt interpret the question well, although ur working was fine :)

Yogesh Verma - 7 years, 2 months ago

and comparatively has only half the price than it should be.... larger pizza has quadraple the area of the smaller one ,,and its cost is only double the smaller pizza..

SaiTeja Muddana - 7 years, 2 months ago

i dont understand the question..

zarree khan - 7 years, 2 months ago

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What is difficult to understand in this question.

Gaurav singh - 7 years, 2 months ago

the larger one is better

rupesh rupesh - 7 years, 2 months ago

I had this question in my PSA exam!

Suyash Mahar - 7 years, 2 months ago
Flávio Sallem
Sep 19, 2015

The bigger pizza has an area of 900 pi cm, while the smaller one has an area of 225 pi cm. The smaller one costs X dollars, and the bigger one 2X dollars. Then:

X = 225pi AND

2X = 900 pi => X = 450pi

Hence, the bigger pizza is twice the area of the smaller pizza for the same price.

Atul Vaibhav
Apr 6, 2014

area of bigger pizza=4*area of larger and cost twice.so the bigger one has better price

Samir Shaheen
Mar 31, 2014

The area of the larger one is 4 times the area of the small one. The area is proportional to radius2 the area 4 times and the price is 2 times. So per uncut area larger on is half price of the smaller one.

Ravi Kaur
Mar 31, 2014

Well , what if the smaller one has bacon in it?

and the bigger ones with pepperoni?

Valerian Pratama - 7 years, 2 months ago
Mhardz Mariquit
Mar 30, 2014

3600:2 > 900:1 that's why 60 cm. pizza has a better value

Lokesh Manikanta
Mar 27, 2014

2*smaller one area=1800pi... bigger one area=3600pi

The value also depends on the toppings, they could be of the same size but different toppings

Mayflor Emmanuel - 7 years, 2 months ago

But even if area of larger is greater but compare area with cost

Shubham Shastri - 7 years, 2 months ago
Ming Song
Mar 27, 2014

Firstly, we have to find the area of each of the pizza. Recall that area of a circle = π x radius² Hence, Area of large pizza = π(30²) = 2830cm² (3 sig. fig) Area of smaller pizza = π(15²) = 707cm² (3 sig. fig) 2830/707 = 4 (1s.f) Since the cost is just double but you get 4 times the amount of pizza, of course the large one is worth it :D

Tasnim Rawat
Mar 26, 2014

Let prize of smaller pizza be x.

Then the prize of larger pizza = 2 x

area of smaller pizza = 707

area of larger pizza = 2828 as this is four times more than the smaller one and the prize is just double.

So the larger pizza is better one.

Kuga Yuuma
Mar 25, 2014

area big one = 4 x area smaller one solver by formula: ( d^2 ) / 4 which d : diameter

Pranav Dixit
Mar 25, 2014

Direct value of diameter should not be taken as basis for money value because for finding the size of pizza, we need square of the radius so the values change a lot after squaring and hence the size of other pizza increases more than 2 times (as thought commonly at first glance)!

Kumar Ujjwal
Mar 25, 2014

volume of pizza received per unit cost will decide which of the two sizes has greater value for money. Now consider the following: 1. Volume of a uniform body= (area) .(thickness) 2. Thickness being the same for two pizzas, volume is dependent on area alone. 3. Pizza being circular, area=[(pi).(d.d)]/4, consider (pi)/4 as a constant, say k 4. So area = k.(d.d) 5. Area of smaller pizza = k.(30.30)= 900k------- (i) 6. Area of larger pizza = k.(60.60) = 3600k-------(ii) 7. We see (ii) is greater that twice of (i). But it costs only twice of (i). 8. That is , you are getting more than twice the area of smaller pizza at just twice its cost. So a bigger pizza is a better deal. Order that one :)

Bhargav Varshney
Mar 24, 2014

Sir, PSA is the short form of Problem Solving Aptitude. It is a test , which comprises of English , mathematics and science. We get marks on the basis of our performance in PSA.

Harsh Bhudolia
Mar 24, 2014

THE VOLUME OF SMALLER PIZZA IS 225 PIH THE VOLUME OF GREATER PIZZA IS 900PIH SO GREATER PIZZA HAS BETTER VALUE

Kartik Gupta
Mar 22, 2014

it is given that thickness is same, therefore the value is to be calculated only on the bases of circular area.In term of price larger pizza is double the smaller while in terms of area larger pizza is four times the smaller.

Nikhil Raj
Mar 22, 2014

as thier thickness are same then find out the ratio between volumes of smaller/larger pizza that is 1/4 . but the ratio between price of smaller/larger pizza is 1/2 . hence the the larger pizza has greater value

Sohail Shaikh
Mar 22, 2014

area of pizza with diameter 30 is 2826 and area of pizza with diameter 60 is 11304. which is very large therefore Large pizza has good value

Laxman Selvam
Mar 22, 2014

the cost/volume of the larger pizza is much less than that of the smaller pizza. hence.

Chanchal Soni
Mar 22, 2014

In just doubling the cost we get 4 times the quantity of smaller Pizza.

As you can get more quantity of pizza with 60 cm diameter than that of the two smaller ones, the greater pizza has good value. More can be got with the same cost.

prakash padhy - 7 years, 2 months ago

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