Question

linear approximation of the volume of a cone - V=(1/3)pi x r^2 x h

Answer 1

Rewritten Equation:
\[V=\frac{1}{3}\pi^2h\]

Answer 2

What is the question?

Answer 3

@Ahsome

Answer 4

i have found that r=6 and h=6

Answer 5

this z is surface area??

Answer 6

i thought z=h?? I'm probably wrong though @aryandecoolest

Answer 7

nopes surely z is not equal to h..... this function describes it's surface area i guess..

Answer 8

to figure out the radius I would write the equation as
\[ \sqrt{4x^2 +8x + 4y^2 -24y +40}= 6-z \]
or after factoring a 4 from the square root (making it a 2)
\[ \sqrt{x^2 +2x + y^2 -6y +10}= \frac{6-z}{2} \\
x^2 +2x + y^2 -6y +10 = \frac{(6-z)^2}{4}
\]
complete the square on both the x and y, by writing 10 as 1+9 and putting 1 and 9 in the "correct spots":
\[ x^2 +2x +1 + y^2 -6y +9 = \frac{(6-z)^2}{4} \\
(x+1)^2 + (y-3)^2 = \frac{(6-z)^2}{4}
\]

that is the equation of a circle with center (-1,3) and radius
\[ r = \frac{6-z}{2} \]
the radius when z =0 (i.e. on the ground), is 6/2= 3

Answer 9

thanks @phi what would h be?

Answer 10

your "h" is correct, h=6

Answer 11

ah right, and r=3, thanks! @phi