Sugar Quest

Geometry Level 3

An ant is trying to get over the top of a Coke can from the starting point $A$ . Its helical red trail is constant in slope and angle before reaching the top edge at point $B$ , which is directly above point $A$ .

If the can has a radius of $4\text{ cm}$ . and is $6\pi \text{ cm}$ . high, what is the total distance the ant has traveled? If your answer is in a form of $C\times\pi\text{ cm}$ , submit $C$ as your answer.

The answer is 10.

1 solution

Worranat Pakornrat
Jan 18, 2016

If we unfold the cylinder into a plain rectangle as shown above, the total red distance AB that the ant has traveled is, in fact, a hypotenuse side of a right triangle, whose base is the can's circumference of radius 4 cm. and height of 6 $\pi$ cm.

The base circumference = 2 $\pi$ r = 8 $\pi$ .

Then by Pythagorean theorem, $AB^2$ = $(8\pi)^{2}$ + $(6\pi)^{2}$ = 100 $\pi^{2}$ .

Hence, AB = $10\pi$ .

The picture is incorrect.

$\overline { AB }$ and, if I let the point which the two lines cross to $C$ , then they should meet together in each spot.

But, they dont meet.

So, the picture is incorrect.

. . - 1 month, 2 weeks ago

Sugar Quest

The answer is 10.

1 solution

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