Question

The volumes of two similar solids are 1000 m and 343 m. The surface area of the larger one is 500 m. What is the surface area of the smaller one?

Answer 1

Is this a multiple choice question or essay?

Answer 2

a) 172m. B) 1715 m. C) 245 m. D) none of these
These are the choices for answer

Answer 3

Suppose the solid has one parameter (radius). Volume is a cubic function of that. The larger volume is \[10^3=1000\] the smaller volume is \[7^3=343\]

Answer 4

Surface is a quadratic function of the same parameter.

Answer 5

I don't understand what you mean. Can you show me equation to figure this?

Answer 6

the ratio of the volumes is \[\frac{343}{1000}=(\frac{7}{10})^3\] so the ratio of the surfaces will be \[(\frac{7}{10})^2=\frac{49}{100}\]

Answer 7

now we know the larger surface is 500

Answer 8

with that and the ratio we can get the smaller surface by multiplying \[\frac{49}{100} 500\]

Answer 9

Does it make sense?

Answer 10

Yes, thank you. That ratio helps so much! I get it now

Answer 11

my pleasure