[aloeverahe]

Hey all
Just want to ask 2 questions that I am currently stuck on in my homework

1. The volume of a sphere varies directly as the cube of its radius. Show that three spheres of a radii 1.8cm, 2.4cm, 3cm are together in volume to one with radius 3.6cm. Prove this statement using variation only.

For this question, I am told to not use the V=4/3pie x r^3 and I must use variation.

This really confuses me because I don't know which one to use and how to write out the equation. As long as someone can tell me the equation, I can go on and work it out myself. Thank you!

2. Andrew takes 'm' days to build a fence which Brian can build in 'n' days. If $K is paid for the job when both work together, how much should Andrew recieve? Use ratio in terms of 'm', 'n' and 'k'.

Same for this one, I'm guessing I'm only stuck on the starting equation, so if you want, just help me find the start and the result and I'll try to work out the rest in the middle.
:)

[ROLCAM]

We are told not to do homework for others !
I thought this was fairly straightforward.
Just proving something.

3.6^3 = 46.656

1.8^3 = 5.832
2.4^3 = 13.824
3.0^3 = 27.000

TOTAL = 46.656

It works. Just adding a few volumes.

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For the second question .
Put some real values FOR m,n and K and see how it works out.

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spelling comment.

I before e , except after c ********so receive.

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[aloeverahe]

We are told not to do homework for others !
I thought this was fairly straightforward.
Just proving something.

3.6^3 = 46.656

1.8^3 = 5.832
2.4^3 = 13.824
3.0^3 = 27.000

TOTAL = 46.656

It works. Just adding a few volumes.

---------------------------------------------------------------------------

For the second question .
Put some real values FOR m,n and K and see how it works out.

---------------------------------------------------------------------------

spelling comment.

i before e , except after c ********so receive.

---------------------------------------------------------------------------

Woah thank you so much!
Haha... yeh, usually I ask my family and friends but I left it until the very last day because I was very busy this week. I know it's not the right thing to do, but I'm desperate :)
So you can just prove the statement like that? I'll have a try.
Hmm, for the second question, I put in real numbers? The problem here is I can put in any number and the answer would be different each time, so what ratio do I use?? Confused.

Oh yeah, and thanks for the little 'English' lesson :)

[ArcSine]

Aloeverahe, the tipoff in your first question is the phrase "... varies directly... ". In the context of your problem question, it means that the volume V of any sphere can be expressed as

for some constant k. That is, the volume of any sphere can be obtained by multiplying the cube of its radius by some number k, and k is the same for every sphere.

To prove the given statement using "variation only", as requested, means that we don't actually compute volumes, or even necessarily know what k is.

Try kicking it off this way:

to express generally the sum of the volumes of the three smaller spheres. (You can replace and with the specific radii you're given at any time.)

Express the volume of the larger sphere in the same way, and then work your way down to an equality. In this way, you've proven the statement using "variation only".

Hope that helped a bit, and best of luck with it.