Question

31. The volume of two similar solids is 1331 m³ and 729 m³. The surface area of the larger solid is 605 m².

What is the surface area, in square meters, of the smaller solid? (1 point)
81
121
305
405
I think it's C.

Answer 1

@xxloserlikemexx, my explanation wasn't clear?

Answer 2

@pfenn1 My computer was lagging and wouldn't let me see it, so I had to close the question and start again. Sorry.

Answer 3

No problem. I just wondered if I just completely missed the boat. I'll be interested to see how @ParthKohli solves it because he (she?) answers in such clear logical manner.

Answer 4

That's what I thought, but my answer wasn't one of the choice, so I picked what was closest.

Answer 5

*choices

Answer 6

The ratio of volumes of similar solids is "a^3/b^3"
The ratio of surface areas of similar solids is "a^2/b^2"

Basically, we have to find a/b using what we know of the volume ratio and then square it for the surface area ratio.
Then we set it equal to "605/x", the known surface area ratio, where the 'x' is just the surface area of the smaller solid.

Answer 7

So, should I put it into proportions?

Answer 8

The answer is 001101000011000000110101

Answer 9

Yeah, that's basically what we're working with here.

\[ \frac{a^3}{b^3} = \frac{1331}{729} \]
We find \(\frac{a}{b}\) by taking the cube root of both sides, and then we square it and place into:
\[ \frac{a^2}{b^2} = \frac{605}{x} \]
and then it's just proportion solving from there.

Answer 10

Here's a little example to help you understand that ratio concept:

I have 2 lines:

One measures 2 units and second one measures 4 units.

The ratio of \(\large \frac{a}{b}\) would be \(\large \frac{2}{4}=\frac{1}{2}\)

Alright, now let's put that into a 2D thing.


The ratio of \(\large \frac{a^2}{b^2}\) would be \(\large \frac{2^2}{4^2}\)=\(\large \frac{4}{16}\) or \(\large (\frac{1}{2})^2\)

Now 3D


The ratio of \(\large \frac{a^3}{b^3}\) would be \(\large \frac{2^3}{4^3}\)=\(\large \frac{8}{64}\) or \(\large (\frac{1}{2})^3\)