An insect is sitting at the bottom of tree that is 20 meters tall. The insect starts to crawl up the trunk of the tree in a regular spiral. It makes 5 rounds of the tree and reaches the top of the tree at a point directly above the point from which it started. If the speed of the insect is 3 cm/s, what is the time (in seconds) it takes to reach the top of the tree from the moment it starts walking up in a spiral? Assume that the trunk of the tree is a right circular cylinder and it takes the insect 1 minute and 40 seconds to crawl around the base of the truck once.
Explanation:
The insect takes 1 minute and 40 seconds = 100 second to crawl around the base of trunk at 3 cm/s. ∴ Circumference of the base = 100 × 3 = 300 cm = 3 meters.
Figure (1) shows the spiral when the insect crawls up the tree.
Now, if we open up the truck, it will make a rectangle (Figure (2)) of height 20 meters and circumference 3 meters.
⇒ From figure AB = 42+32 = 5 meters
⇒ From figure the total distance travelled by the insect = 5 × 5 = 25 meters = 2500 cm.
∴ Time taken by the insect = 25003 seconds.
Hence, option (a).
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