5. What are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of .8L?
That depends upon how thick you make the walls of the cone. They should have asked for the minimum surface area cone with that volume.
The surface area of a cone is:
A = pi s r
= pi*sqrt(r^2 + h^2)*r
where s is the slant height and h is the height of the axis.
The cone volume must satisfy (1/3)pi*r^2*h = 800 cm^3, so
h = 2400/(pi*r^2)
Write A as a function of r only and differentiate A(r). Set the derivative equal to zero and solve for r.
To determine the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 0.8L, we need to consider the formula for the volume of a cylinder, which is given by V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder.
First, let's convert the volume from liters to cubic centimeters (cm³) since the units for the radius and height should be in centimeters as well. We know that 1L is equal to 1000cm³.
So, 0.8L * 1000cm³/L = 800cm³.
Now, let's determine the radius and height of the cylinder. Since we want to minimize the weight of the can while maintaining the given volume, we need to find the dimensions that minimize the surface area of the can. The surface area formula of an open-top cylinder is A = 2πrh + πr².
To minimize the surface area, we need to minimize both the height and the radius while maintaining the given volume.
8. What is the third planet from the sun?