BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Volume and surface area

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 94
Joined: Sun Aug 29, 2010 3:40 am
Thanked: 3 times
Followed by:1 members

Volume and surface area

by leonswati » Fri May 18, 2012 4:58 am
A certain object has a volume of 216 cubic centimeters and a surface area of 240 square centimeters. Another object is a smaller-scale replica of the original object. If the surface area of the smaller object is 60 square centimeters, what is its volume?
Swati
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 142
Joined: Thu Apr 26, 2012 3:24 am
Location: India
Thanked: 28 times

by mathbyvemuri » Fri May 18, 2012 5:50 am
As the formulae for S.A and Volume of the two objects are identical, the ratios of SA to Volume of the two objects are same.
V of smaller one/SA of smaller one = V of bigger one/SA of bigger one
=> V of smaller one/60 = 216/240
=> V of smaller one = 216*60/240 = 54

There is a flaw in this solution and the correct one is presented in my later post in this thread
Last edited by mathbyvemuri on Fri May 18, 2012 8:26 am, edited 2 times in total.
Top
Master | Next Rank: 500 Posts
Posts: 142
Joined: Thu Apr 26, 2012 3:24 am
Location: India
Thanked: 28 times

by mathbyvemuri » Fri May 18, 2012 5:50 am
deleted
Last edited by mathbyvemuri on Fri May 18, 2012 8:08 am, edited 2 times in total.
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 94
Joined: Sun Aug 29, 2010 3:40 am
Thanked: 3 times
Followed by:1 members

by leonswati » Fri May 18, 2012 5:53 am
The answer is 27
Swati
Top
Master | Next Rank: 500 Posts
Posts: 142
Joined: Thu Apr 26, 2012 3:24 am
Location: India
Thanked: 28 times

by mathbyvemuri » Fri May 18, 2012 8:04 am
yes there is a correction here:
to take care of the dimensions
V^(1/3)/SA^(1/2) ratios for the two objects must be equal
=> V^(1/3)/60^(1/2) = 216^(1/3)/240^(1/2)
=> V^(1/3) = 6/2 = 3
=> V = 3^3 = 27

The logic is here:
Unit of V is cm^3
Unit of SA is cm^2
In order to get the dimensionless ratio, we take ratio of cube root of V to the square root of SA.
Top
Post new topic Post Reply
• Page 1 of 1