A conical drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup
link of picture of the cup is found in the attachement
A conical drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup
link of picture of the cup is found in the attachement
Hello, aaasssaaa!
A conical drinking cup is made from a circular piece of paper of radius
by cutting out a sector and joining the edges and
Find the maximum capacity of such a cup.Code:..*.*.*.. .*:::::::::::*. A*:::::::::::::::*B * *:::::::::::* * R *:::::::* R * *:::* * * * * * C * * * * * * * * * *
The side view of the cup looks like this:Code:r *-----+-----* \ : / \ h: / \ : / R \ : / \:/ *
where is the radius of the cone and is its height.
We see that: . [1]
The volume of a cone is: . [2]
Substitute [1] into [2]: .
Maximize
. . and we get: .
Substitute into [1]: .
Substitute into [2]: .
Therefore, the maximum volume is: .