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Mathematics 14 Online
Nicole:

http://prntscr.com/ir4n5s

Nicole:

@Vocaloid @563blackghost

Nicole:

is this correct?

563blackghost:

You equation is setup correctly but your product is incorrect.

Nicole:

Oh is it. 603.19

563blackghost:

If you keep it in terms of pi then yes. Are suppose to keep it as \(\bf{\pi}\) or as 3.14?

Nicole:

Keep it as is

Nicole:

How about this: http://prntscr.com/ir4qt2

563blackghost:

Also make sure your answer ends as: \(\large\bf{V=603.19 ~ cm^{2}}\) otherwise you might get it wrong.

Nicole:

Ohh ok

563blackghost:

really crucial to have your units defined otherwise you might get your entire problem wrong even if your calculations are correct.

Nicole:

Yes that actually happened before lol

563blackghost:

For the next one you need to know your formula for a volume of a prism: \(\large\bf{V=lwh}\) You know `h=10` and `w=5` and well as the volume wanting to be `200`. So we plug in our info. \(\large\bf{200=l(10)(5)}\) Now we simplify to find `l`. \(\bf{200=l(50)}\) \(\bf{\frac{200}{50} = l}\) What is `l`?

Nicole:

l is 4

563blackghost:

yup

Nicole:

http://prntscr.com/ir4vv5

563blackghost:

First find the volume of the given dimensions. Then you want to try doubling one dimesions each time. \(\large\bf{8×9×16 ~~~~, ~~~ 4×18×16 ~~~~ ,~~~ 4×9×32}\) After that try and divide the doubled dimension by the original. What do you see occurring?

Nicole:

So the volume is 576

Nicole:

Now, do I multiply all the pairs you put?

563blackghost:

try each out, yes.

Nicole:

When I multiplied each one, they all ended up with 1152 as the product.

563blackghost:

Yes that is correct. Now try and divide the outcome by 576. What is it increasing by?

Nicole:

the answer for that is 2

563blackghost:

So this tells you if you increase one dimension the volume will double as well.

Nicole:

Ohh ok...you really smart LOL

563blackghost:

>.< well thank you, but i still got much to learn though ;)

Nicole:

Same here LOL. http://prntscr.com/ir5221

Nicole:

I know the formula is: V=a^2*h/3

563blackghost:

To find the volume of a square pyramid you need to use the formula: \(\bf{V=a^{2} \frac{h}{3}}\) The `height is 455.4` and the `base (a) is 755.9` Plug this in. \(\large\bf{V=755.9^{2} \frac{455.4}{3}}\)

Nicole:

Ok so first divide the fraction

563blackghost:

yea

Nicole:

151.8 and multiply that by 755.92^2

563blackghost:

yes

Nicole:

http://prntscr.com/ir54qw This is what I got LOL

563blackghost:

Did you plug this in a calculator?

563blackghost:

Cause my outcome was different. I got \(\bf{86736214.16}\)

Nicole:

I used mathway

Nicole:

If you round your answer, it will become my answer

Nicole:

Does that make sense LOL

Nicole:

@563blackghost

563blackghost:

hrmmmm did you round the terms before the simplification?

Nicole:

no I just multiplied...I guess its automatic.

563blackghost:

oh okie... well i plugged in the equation into my calculator then double checked with mathway but the outcome is the same for meh....

Nicole:

So should I use your answer or my answer or both?

563blackghost:

hrmmmm it would be best for a second opinion to see if they get the same outcome.

Nicole:

Ok I can do that later....Can we move on tho?

563blackghost:

sure

Nicole:

http://prntscr.com/ir5eg1

563blackghost:

Do you know your surface area equation for a prism?

Nicole:

umm...noo

563blackghost:

The equation is: \(\bf{A=2(wl+hl+hw)}\) First you would find the surface area of the given dimensions then try with one dimension being doubled. \(\bf{2(4(6) + g(6) + 6(4))~~~,~~~2(8(3)+6(3)+6(8)~~~,~~~2(3(4)+12(3)+12(4)}\) What do you see occurring?

Nicole:

Ok so first, A=(4*3+6*3+6*4)

563blackghost:

make sure to include the 2.

Nicole:

oh ok

Nicole:

108

563blackghost:

yea that is right

Nicole:

I cant see all the pairs...Can you write it again please?

563blackghost:

\(\bf{2(4(6) + 6(6) + 6(4))}\) \(\bf{2(8(3)+6(3)+6(8))}\) \(\bf{2(3(4)+12(3)+12(4))}\)

Nicole:

http://prntscr.com/ir5xya

Nicole:

Thats my answers

Nicole:

What do I do now?

563blackghost:

So now you would compare if the original surface area really is doubled if one of the dimensions is doubled. Your original surface area is `108`. `108 x 2 = 216` Do any of the pairs equal to 216?

Nicole:

No none of them

Nicole:

So they cannot be doubled?

563blackghost:

Correct they aren't. So yes, if the doubling of one dimension occurs the surface area does not double.

Nicole:

Okie. http://prntscr.com/ir62xa One more after this please

Nicole:

@563blackghost

563blackghost:

Use this formula for surface area: \(\large\bf{A=2 \pi rh + 2 \pi r^{2}}\) Plug in your given info. \(\large\bf{A=2(3.14)6(11.5)+2(3.14)(6^{2})}\)

Nicole:

The answer is 659.4

Nicole:

Correct?

563blackghost:

yea that is right

Nicole:

Last one: http://prntscr.com/ir6a1w

Nicole:

@563blackghost

Nicole:

@563blackghost

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