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1. Volume and surface area of similar shapes
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?
Last edited by krisshP; 02-06-2012 at 18:11.
2. Re: Volume and surface area of similar shapes
(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 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
3. Re: Volume and surface area of similar shapes
(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 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.

Thanks a lot for helping me out.
4. 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