Posted by **alisa** on Tuesday, November 15, 2011 at 8:09pm.

If the ratio of the volume of two similar solids is 8:125, then what is the ratio of their surface areas?

- geometry -
**bobpursley**, Tuesday, November 15, 2011 at 8:19pm
lets take a rectangular solid, in the form of a long prism.

V=bhl

Area= 2(bh+lh+bl)

let l= 8, b=8h

so, for v=8, l=8, b,h=1

now scale it up to 125/8

l=8*cubrt(125/8)=8*5/2=40

b= 5/2 h=5/2

original surface area: 2(1+8+8)=34

new surface area: 2(25/4+200/2+200/2)

= 2(412.5/2)=412.3

ratios of surefce area 34:412.3

Now you need to figure other shapes. Try a cube, and a sphere.

- geometry -
**Steve**, Wednesday, November 16, 2011 at 12:39am
If two solids have volume ratio r^3, then

their linear ratio (sides length) is r

their area ratio (surface area) is r^2

So, since

v/V = (2/5)^3

a/A = (2/5)^2 = 4/25

You gained a factor of 2 there when you said 8*5/2 = 40

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