# math

posted by .

find the radius and height of a cylindrical soda can with a volume of 21in^3 that minimize the surface area.

• math -

height --- h
given: πr^2 h = 21
h = 21/(πr^2)

Surface area (SA) = 2πr^2 + 2πrh
= 2πr^2 + 2πr(21/(πr^2)
= 2πr^2 + 42/r
d(SA)/dr = 4πr - 42/r^2
= 0 for a max/min of SA
4πr = 42/r^2
r^3 = 42/(4π)
r = (42/(4π)^(1/3) = 1.495163.. or appr 1.5
then h = 21/(πr^2) = 2.99027 or appr 3

notice the h = 2r

## Similar Questions

1. ### algebra/geometry please correct me

You need to make a soda can with a volume of 29 cubic inches. Find the surface area. calculate the following: a) How much material is needed if the can's radius is 2 inch?
2. ### geometry/algebra

I asked this question yesterday, and I'm trying to understand it since I got the wrong answer - please explain: You need to make a soda can with a volume of 29 cubic inches. Find the surface area. calculate the following: a) How much …
3. ### math

the volume of an cylindrical can with a radius r cm and height h cm is 128000 c^3, show that the surface area of the can is A=2(22/7)r^2 + 246000/r. Find the value for r to minimize the surface area. *i know what the quest. ask but …
4. ### Math 11 Surface area, Volume and Capacity

A cylindrical tin can has a radius of 4.5cm and a height of 5 cm (a)What is the surface area of the can (b)What is its volume?
5. ### maths --Surface area and all that..

A toy is in the shape of a right circular cylinder with hemisphere on one end and a cone on the other . The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radius of the hemispherical and conical parts …
6. ### Math

Optimization Problem A right circular cylindrical can of volume 128tπ cm^3 is to be manufactured by a company to store their newest kind of soup. They want to minimize the surface area of the can to keep costs down. What are the …
7. ### geometry

a cylindrical soup can has a volume of 335cm^3.find the dimensions(radius r and height h)that minimise the surface area of such a can.
8. ### Calculus

A company needs to make a cylindrical can that can hold precisely 1.5 liters of liquid. If the entire can is to be made out of the same material, find the dimensions (radius and height) of the can that will minimize the cost. Round …
9. ### math

3.A rectangular prism has a width of 92ft and a volume of 240ft.Find the volume of a similar prism with a width of 23ft.Round to the nearest tenth, if necessary. 4.A pyramid a height of 5in. and a surface area of 90in^2.Find the surface …
10. ### Math

A manufacturing company wants to minimize the cost of materials for a pop can which needs to hold 640 mL. Find the radius and height (in centimeters) of the cylindrical can with minimum surface area that holds this volume. Give your …

More Similar Questions