Asked by jasmine22
cylindrical box will be tied up with ribbon
as shown in the figure. The longest piece of ribbon available
is 130 cm long, and 10 cm of that are required for the bow.
Find the radius and height of the box with the largest possible
volume.
as shown in the figure. The longest piece of ribbon available
is 130 cm long, and 10 cm of that are required for the bow.
Find the radius and height of the box with the largest possible
volume.
Answers
Answered by
Steve
assuming the ribbon is tied on top, and holds on the lid, its length will be
2h+2d + 10 = 130
h+2r = 60
So, since v = pi r^2 h,
v = pi r^2 (60-2r)
= 60pi r^2 - 2pi r^3
dv/dr = 120pi r - 6pi r^2
= 6pir(20-r)
dv/dr=0 at r=20
So, the box has
radius = 20
height = 20
2h+2d + 10 = 130
h+2r = 60
So, since v = pi r^2 h,
v = pi r^2 (60-2r)
= 60pi r^2 - 2pi r^3
dv/dr = 120pi r - 6pi r^2
= 6pir(20-r)
dv/dr=0 at r=20
So, the box has
radius = 20
height = 20