Question

attache file

Answer 1

my anwer is the same your but the key is 9cm ,I hope the key is wrong

Answer 2

The height of the cone is h = x+ 15. The radius of the cone (not the radius of the sphere) is:\[r = \sqrt{15^2-x^2}\]using the pythagorean theorem, So the volume of the cone is going to be:\[V = \pi r^2h = \pi (\sqrt{15^2-x^2})^2(15+x) = \pi (225-x^2)(15+x) = 1152\pi\]\[\Longrightarrow (225-x^2)(15+x) = 1152\]Now all thats left is to solve this equation.

Answer 3

oops, i forgot to divide by 3. The formula for the volume of a cone is:\[V=\frac{1}{3} \pi r^2 h\]

Answer 4

So the actual equation should be:\[\frac{1}{3}(225-x^2)(15+x) = 1152\]or\[(225-x^2)(15+x) = 3456\]

Answer 5

There are two possible answers (apart from a negative value):
3sqrt(17)-12, and 9.
So the key is still correct.

Answer 6

how you solve answer is 9 ?

Answer 7

The base radius is sqrt(15^2-x^2), the height is 15+x, so
(1/3)pi(15+x)(15^2-x^2)=1152pi
-x^3-15x^2+225x-81=0
Wouldn't it be tempting to try x=9?

Answer 8

The topic is the Rational Roots theorem, so if this equation has a rational (or integer for that matter) root, it has to be a divisor of 81. So you would try things like 3, 9, 27, etc. Turns out 9 works.

Answer 9

Thank all your guy

Answer 10

You're welcome!

Answer 11

I just realized that I have butt in the middle of your discussion, sorry Joe.

Answer 12

no worries, you didnt lol