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Geometry Level 2

I have 2 cups which are similar to each other. They have surface areas of 60 60 cm 2 ^2 and 135 135 cm 2 ^2 . If the base area of the smaller cup is 16 16 cm 2 ^2 , what is the base area of the larger cup (units of cm 2 ^2 )?


The answer is 36.

Chung Kevin by Chung Kevin , 45, Australia

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10 solutions

Niraj Sapkota
Dec 15, 2013

135/60=x/16 where 'x' is the are of the base

7 Helpful 0 Interesting 0 Brilliant 0 Confused

nice..:)

Victor Almeral Jr - 7 years, 5 months ago
Walidur Mridul
Dec 16, 2013

suppose the base area of the larger cup is 'X' cm2 then; 60/16=135/X; so, X=36

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Clever. I made a small mistake and my answer went wrong xD

Sukant Panigrahi - 7 years, 5 months ago

Hello everyone! First of all,The exercise said that both cups are similar,so they are proportional. Hence :

60 = the surface area of the smaller cup;

135 = the surface area of the bigger cup;

16 = the base area of the smaller cup;

x = the base area of the bigger cup;

Than We have to find the proportion between them : 135 / 60 = 2.25

than we have the conclusion that the bigger is 2.25 bigger than the smaller.

than,2.25 x 16= 36 cm².

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Avro Rahman
Dec 19, 2013

Suppose ,the base area of the larger cup is 'x'. so (135/60)=(x/16) or, 60x=2160 so the value of 'x' is 36

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Dashvin Kaur
Dec 17, 2013

60 DIVIDE BY 16=3.75 135 DIVIDE BY 3.75=36

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Enzo Til-Am
Mar 1, 2014

By ratio and proportion :))

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Shreya R
Feb 18, 2014

It is said that the two cups are SIMILAR- meaning that the ratios of the two are equal. Thus we get the equation 135/60=x/16. Thus by solving x, we obtain 36 as the answer

0 Helpful 0 Interesting 0 Brilliant 0 Confused
John Palmer
Jan 6, 2014

Since the surface areas are similar you can put them into a ratio, 60:135 (4:9). This similarity also means that the base areas can be put into a ratio, 16:x. In order to be similar the ratios have to correspond to one another, meaning that 4:9 has to be multiplied by 4 on both sides to become a 16:36 ratio. The 36 is the base area of the other cup.

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Shankhadeep Dey
Jan 3, 2014

16 * X=60 X=60/16=15/4 Y ( remember it's the base area of the larger cup) so, Y 15/4=135 Y=135 4/15=9*4=36... the answer 36...

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Nishchay Selot
Dec 26, 2013

we do this simply by proportion. 16 : 60 :: x : 135 where x is the base area of the larger cup.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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