the volume of a cylindrical tin can with a top and a bottom is to be 16*pi cubic inces. if a minimum amont of tin is to be used to construct the can, what must be the height, in inches, of the can?
volume of cyliner is pi*r^2*h
do i like take derivitive of something since it talks about minimum. please help me. i don't get this
you want to minimize surface area.
Area= 2*2PIr + h*2PIr
but h= V/Pir^2
TAke dA/dr, set to zero, solve for r.
Then solve for h in the volume equation.
I need to know how to get the total surface area of a cylinder. The way that I get the lateral area is by taking by info for example 5cm x 12cm 60x3.14x2 =376.8cmsquared but I am trying to get the total area.
set volume=16pi, solve for r
then substitute r in for the surface area equation (2pirh+2pir^2)
take the derivative
find critical point (where derivative=0)
then make sure that is a minimum
To find the total surface area of a cylinder, you need to consider the curved surface area (lateral area) as well as the areas of the top and bottom circles.
The formula for the lateral area (curved surface area) of a cylinder is:
Lateral Area = 2πrh
The formula for the area of a circle is:
Circle Area = πr^2
To find the total surface area of the cylinder, you need to add the lateral area to the sum of the areas of the top and bottom circles:
Total Surface Area = Lateral Area + 2(Circle Area)
So the formula for the total surface area of a cylinder is:
Total Surface Area = 2πrh + 2(πr^2)
By substituting the given values into the formula, you can calculate the total surface area of the cylinder.
To find the total surface area of a cylinder, you need to consider both the lateral area and the areas of the two circular bases.
1. Lateral Area:
The lateral area of a cylinder is the curved surface area that wraps around the cylinder. It can be calculated by multiplying the height (h) of the cylinder by the circumference of the circular base (2πr, where r is the radius of the base). So, the formula for the lateral area is:
Lateral Area = 2πrh
2. Circular Base Areas:
The circular bases of the cylinder are identical and can be calculated using the formula for the area of a circle, which is πr^2.
Now, to find the total surface area, you need to add the lateral area to the sum of the two circular base areas:
Total Surface Area = Lateral Area + 2(Base Area)
= 2πrh + 2(πr^2)
= 2πr(h + r)
Remember that r is the radius of the base, and h is the height of the cylinder.
By finding the total surface area, you will have a complete understanding of the shape and size of the cylinder.