A fly lands on the outside of a cylindrical

drinking glass 6 cm from the top. Dia-

metrically opposite the fly and 7 cm from

the bottom, but on the inside of the glass,

there is a drop of honey. The glass has

circumference 24 cm, height 10 cm. Find

the shortest path, in cm, that the fly must

walk on the surface of the glass to reach

the honey.

kijijij Apr 11, 2020

#1

#3**0 **

OK....I think there is a shorter way anyway.....I think it is 15 cm.....diagram to follow.

ElectricPavlov
Apr 11, 2020

#4**0 **

Start with the type of picture drawn by EP -- respresenting the unrolled cylinder as a rectangle.

Place this rectangle upon a coordinate grid with the

-- bottom-left corner at (0,0)

-- bottom-right corner at (24,0)

-- top-left corner at (0,10)

-- top-right corner at (24,10)

-- fly at (24,4)

-- drop of honey at (12,7)

Moving from fly to honey will be the distance sqrt(12^{2} + 3^{2}) = sqrt(153)

[you can draw a right triangle and use the Pythagorean Theorem or use the distance formula]

geno3141 Apr 11, 2020

#5**0 **

I don't know if that will work.....the honey is INside the glass....the fly is on the OUTside.

ElectricPavlov
Apr 11, 2020

#6**+1 **

Unroll the glass cylinder to make a rectangle .....then reflect the image(to make for the fact the fly must cross over the lip of the glass to the inside) to make a double rectangle ....then use the measurements to calculate the distance

sqrt (12^2 + 9^2) = 15

ElectricPavlov Apr 11, 2020