Friday

April 18, 2014

April 18, 2014

Posted by **Anonymous** on Wednesday, June 4, 2008 at 9:24pm.

Work:

V=(pi)r^2(h)

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

2(pi)r + h=30

V=(pi)r^2(h)

V'=2(pi)(r)h+2pi(r^2)=0

- Calculus -
**Damon**, Wednesday, June 4, 2008 at 9:56pmh + 2 pi r = 30

so

h = 30 - 2 pi r

dh/dr = -2 pi

pi r^2 h = v

so yes

dv/dr = pi r^2 dh/dr + h (2 pi r) dr/dr

so

dv/dr = pi r^2 (- 2 pi) + 2 pi r h

that is 0 for maximum of minimum

2 pi^2 r^2 =2 pi r h

pi r =h

r = h/pi

then

h = 30 - 2 pi r = 30 - 2 pi (h/pi)

h = 30 - 2 h

3 h = 30

h = 10

r = 10/pi

- Calculus -
**drwls**, Wednesday, June 4, 2008 at 9:59pmYou have to make V a function of r only abd then set the derivative equal to zero.

V = pi r^2 h

h = 30 - 2 pi r

V = pi r^2 * (30 - 2 pi r)

= 30 pi r^2 - 2 pi^2 r^3

dV/dr = 60 pi r - 6 pi^2 r^2 = 0

divide both sides by 6 pi r

10 - pi r = 0

r = 10/pi

Check my math

- Calculus -
**Anonymous**, Wednesday, June 4, 2008 at 10:39pmThanks Damon and drwls!

**Related Questions**

Calculus - Find the radius, volume, and hieght of the right- circlar cylindar ...

calculus - A potter forms a piece of clay into a right circular cylinder. As she...

Calculus - A cylinder is inscribed in a right circular cone of height 5.5 and ...

Calculus - A cylinder is inscribed in a right circular cone of height 8 and ...

math - Okay. So i'm doing this project for my geometry class about different ...

Geometry - Can someone please check these for me. I have to leave answers in Pi...

ap Calculus - A right circular cone has a fixed slant height, s= 12 inches. ...

calculus - The radius of a spherical balloon is increasing at a rate of 2 ...

Calculus - Gravel is being dumped from a conveyor belt at a rate of 10 cubic ...

calculus - Gravel is being dumped from a conveyor belt at a rate of 50 cubic ...