# More expanding and simplifying and finding volume

• Jan 5th 2010, 07:32 AM
Mukilab
More expanding and simplifying and finding volume
1)Expand and simplify
$\displaystyle n^2+(n-1)^2$ I got $\displaystyle n^4-2n+1$????

If n is a whole number show that this expression must be an odd number. From my previous post would this be the answer: (3n)(76)

2)The radius of a sphere is 3y cm
The radius of a cylinder is 2y cm and the cylinder's height is H cm
The volume of the sphere is equal to the volume of the cylinder
Express the Height (H) of the cylinder in terms of y. Write in the simplest form. No idea how to do this. Please show me a method
• Jan 5th 2010, 07:49 AM
vonflex1
1. $\displaystyle n^2+(n-1)^2 = n^2 + n^2 - 2n +1 = 2n^2 - 2n + 1$

and proving it is an odd number is easy -

$\displaystyle 2n^2$ is even because of the two in the front
$\displaystyle 2n$ is even because of the two in the front
and the remaining $\displaystyle 1$ makes it odd.

2. volume of sphere = $\displaystyle 4/3\pi r^3$
volume of cylinder = $\displaystyle \pi r^2H$ where H is the height.

comparing the two:
$\displaystyle 4/3\pi (3y)^3 = \pi (2y)^2 H$
$\displaystyle 4/3\pi 27y^3 = \pi 4y^2 H$
$\displaystyle H = (4/3) * (27/4) *y$
$\displaystyle H = 9y$
• Jan 5th 2010, 07:59 AM
Mukilab
Thank you for this, a very good and clear post. But please could you explain how you got volume of sphere = http://www.mathhelpforum.com/math-he...2174a18a-1.gif?

I understand everything else including getting the answer at the end
• Jan 5th 2010, 08:13 AM
vonflex1
this formula is the formula for volume of a sphere...

you should take it "for granted"...

if you want i can prove it for you here,

it isn't complicated but i don't think it's required by you...
• Jan 5th 2010, 08:17 AM
Mukilab
That's ok, google finally bestowed me with such information