Volume and surface area of similar shapes
Maths and statistics discussion, revision, exam and homework help.
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Volume and surface area of similar shapesHere is the question I need help on:
The volumes of two mathematically similar solids are in the ratio 27:125.
The surface area of the smaller solid is
.
Work out the surface area of the larger solid.
Here is all my working out:
I divided by 25 to form:
The scale factor for volume for small to big solid is the following:
I now cube root this scale factor for volume to get the linear scale factor:
![\sqrt[3]{4.6296......}](http://www.thestudentroom.co.uk/latexrender/pictures/55/55e6a01db6ae0c0a4f297945377a6048.png "\sqrt[3]{4.6296......}")
As the result of this operation I get:
To get the surface area scale factor for small to big solid I have to square the above:
I end up getting:
So I got
for the surface area of the larger solid. The real correct answer is somehow 
. Where did I go wrong in my working out?
Last edited by krisshP; 02-06-2012 at 18:11. -
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Re: Volume and surface area of similar shapesI did the question and I got the same answer as you. So either we're both making the same mistake or the answer in the book is wrong(Original post by krisshP)
Here is the question I need help on:
The volumes of two mathematically similar solids are in the ratio 27:125.
The surface area of the smaller solid is.
Work out the surface area of the larger solid.
Here is all my working out:
I divided by 25 to form:
The scale factor for volume for small to big solid is the following:
I now cube root this scale factor for volume to get the linear scale factor:
As the result of this operation I get:
To get the surface area scale factor for small to big solid I have to square the above:
I end up getting:
So I got for the surface area of the larger solid. The real correct answer is somehow . Where did I go wrong in my working out?
I think the answer in the book is wrong, though because the larger solid somehow has a smaller surface area than the smaller solid if we go by the answer of the book
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Re: Volume and surface area of similar shapesThanks for helping me out. Not often is my book wrong, but sometimes it can be. This time it's wrong and I just wanted to check so that if I've made a mistake I can correct myself and learn.(Original post by usycool1)
I did the question and I got the same answer as you. So either we're both making the same mistake or the answer in the book is wrong
I think the answer in the book is wrong, though because the larger solid somehow has a smaller surface area than the smaller solid if we go by the answer of the book
Thanks a lot for helping me out.
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Re: Volume and surface area of similar shapes(Original post by krisshP)
So I got for the surface area of the larger solid. The real correct answer is somehow . Where did I go wrong in my working out?
urgh
why didn't you use the fact that 27 and 125 are both cubes
Vfactor = 27:125
Sfactor = 3:5
Afactor = 9:25
Afactor = 36:100
Your answer is correct but I did not like the method
