A geometry problem by Milind Joshi

Geometry Level pending

An ant is climbing in a helical manner on a tree trunk. The height of the tree trunk is 300 m and the girth of the trunk is 40 m. In each helical the ant covers a height of 75m in vertical direction. Can you tell what distance will the ant travel before she reaches the top of the tree?


The answer is 340.

Milind Joshi by Milind Joshi , 27, India

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2 solutions

Milind Joshi
Jun 19, 2014

We can imagine a right angle triangle with height 75m and base as 40m hence the hypotenuse will be the path of ant. That is 75^2 + 40^2 = 85^2

Hence per helical distance travelled is 85m so in total there are 300/75 = 4 helical . hence total distance travelled is 85x4 = 340

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Gwen Roberts
Sep 6, 2015

One helix is the diagonal of a rectangle with dimensions 40 by 75, which is 85. For a cylinder 300 ft high there are 4 of these, so the distance traveled is 4 of these diagonals: 4x85 is 340

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Good observation of the 40-75-85 right triangle.

Thanks! Any tips are appreciated!

Gwen Roberts - 5 years, 9 months ago

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