Help with non calc qs

[daring osprey]

How would you answer this without a calcuator. This is non calc

[runic wagon]

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[daring osprey]

I cant seem to answer this without a calcualtor

[pale onyx]

Note that areas of similar shapes scale as squares of the ratio of their linear sizes.
So, if the ratio of radii is k, then the ratio of areas is k^2.
Same for volumes, but they scale as k^3.

[daring osprey]

How would that help me answer it

[pale onyx]

Well, you know the ratio of volumes of A and B and you can find the ratio of radii of B and C.

[daring osprey]

Wait a minute lemme find my answer now

Is it this

[pale onyx]

Well, I prefer to solve problems like this more generally.
Suppose r2/r1 = a and r3/r2 = b. We have:
V2/V1 = a^3
(r3 - r2)/r2 = b - 1
So, you just solve those for a and b, and the needed ratio is S(C)/S(A) = (ab)^2.

[pale onyx]

Not really sure what exactly you're doing. I just see some numbers.

Use formulas.

[daring osprey]

For A and C i used the SA of a sphere which js 4pi x r squared

[pale onyx]

Again, I can't really verify your approach unless you write formulas, not just numbers.

[daring osprey]

Ok give me 1 minute

[pale onyx]

Radus of C is incorrect.

It's not 50% of the radius of B, it's 50% bigger than it.

[daring osprey]

It says on the question the radius of c is 50% of radius of b

[pale onyx]

Oh, hold on.

Ah, yeah, sorry 😅

The text is a bit blurry, I misread.

[pale onyx]

Well, that's correct apart from the last step. 64/25 obviously isn't 64.25.

[daring osprey]

64:25

[pale onyx]

No, I mean, either leave it as 64/25 or convert it to a decimal fraction, but correctly.

[eager lodge]

@daring osprey

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