# ap Calculus

posted by on .

A right circular cone has a fixed slant height, s= 12 inches. Determine the radius and the height of the cone with maximum volume

• ap Calculus - ,

volume of cone is

V=4/3(pi)r^2h

s^2=r^2+h^2 or s^2-h^2=r^2

V=4/3(pi)(s^2-h^2)h

if 4/3(pi)=k

V=k(144-h^2)h

V=144kh-kh^3

volume is a max when dV/dh is zero

dV/dh = 144k-3kh^2

144k-3kh^2 = 0

144k = 3kh^2
48=h^2

this gives you h, from which you can find r from

s^2-h^2=r^2

please check my maths!

• ap Calculus - ,

I am sure that Dr Russ meant to type

volume of cone is

V=1/3(pi)r^2h

• ap Calculus - ,

Yes oops!

### Answer This Question

 First Name: School Subject: Answer:

### Related Questions

More Related Questions

Post a New Question
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}