Melody

Hi Jedithious,

It is always great to see you in the forum!  

1) The ratio of the surface areas of two cubes is 64:81. What is the ratio of the edges of the cubes?

the answer will just be sqrt(64):sqrt(81) = 8:9

Now I will show you why

$$\dfrac{6l_1^2}{6l_2^2}=\frac{64}{81}\qquad so \qquad \dfrac{l_1^2}{l_2^2}=\frac{64}{81}\qquad so \qquad \dfrac{l_1}{l_2}=\frac{8}{9}$$

2) If the ratio of the volumes of two similar cylinders is 125:27, what is the ratio of their surface areas?

volume is U3,  Surface area is U2

so ratio of surface areas will be  125^(2/3):27^(2/3) = 25:9

3) A model of a rocket was built to a scale of 1:40. 

a) The length of the model was 75 cm. What was the length of the actual rocket, in metres?

75*40=3000cm=30m

b) The area of metal used to cover the curved surfaces of the model was 2750 cm². What area of metal covered the curved suraces of the actual rocket, in square metres?

1:1600 = 2750:2750*1600=4,400,000cm²=440m²     (Little edit here)

c) The nose cone of the rocket had a volume of 96 m³. What was the volume of the nose cone of the model, in cubic centimetres?

1:40³ = x:96  

$$\frac{1}{64000}=\frac{x}{96}\\\\
96\times \frac{1}{64000}=x\\\\
x=1.5\times 10^{-3}\quad m^3$$

100cm in a metre

100³cm³ in a m³

$$x=1.5\times 10^{-3}\times 10^6 = 1.5\times 10^{3} = 1500cm^3$$

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NOW I have taken shourt cuts (maybe I am not allowed to) and my answers are different from CPhill if I get time I will check the long way but I think one of the other mathematicians will validate one of our answers before then. 

Sunday 15/6/14

I put both these posts up to promote discussion.

That is really nice of you Strider.  You certainly did not need to appologise for this post.

Welcome to the forum.  I know you have been here for awhile but now it is official!

I hope that you continue to learn lots and to have a good time here!

Here is some more starter points.

Melody.

$${\frac{{\mathtt{1}}}{{\mathtt{5}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\mathtt{20}}$$

I use this method all  the time!  It is the BEST way to do it!

Factoring trinomials using the grouping method.  

This is a really good clip. 

do you actually mean

f(x)=x+(1/x)-2  

which is what you have written

OR

do you mean

f(x)=(x+1)(x-2)

Really Ninja?  I'd like to hear more.

I love trains!

Not a problem - I thought he might have.

I have already written quite a lot for this - they in the sticky topics already - there are actually 2 of them that need amalgamation.

Let me see.

Here is the newest one that I did yesterday

Well he probably did get it then. Ask him maybe.