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# Locked: Grade 9 math tutor Q

• Last Updated:
• Feb 4th, 2023 6:49 pm
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[OP]
Sr. Member
Nov 25, 2008
815 posts
YORK

## Grade 9 math tutor Q

hi , wonder if someone can help on this math tutoring Q.

A coin with a diameter 1 cm rolls around the outside of a regular hexagon with a side length of 1 cm (as shown on the attached photo ).

What is the length (in cm) of the path traced out by the centre of the coin after one complete rotation around the hexagon ?

Thanks
TC
5 replies
Jr. Member Oct 3, 2022
188 posts
The length of the path traced out by the center of the coin can be calculated by multiplying the circumference of the coin by the number of times it makes a complete rotation around the hexagon.

The circumference of a circle with diameter 1 cm is π cm. The number of complete rotations made by the coin around the hexagon is equal to the number of sides of the hexagon, which is 6.

Therefore, the length of the path traced out by the center of the coin is:

π * 6 = 6π cm

So the length of the path traced out by the center of the coin after one complete rotation around the hexagon is 6π cm.
Deal Fanatic Dec 3, 2004
7110 posts
ChatGPT wrote: The circumference of the coin is pi times its diameter, or approximately 3.14 cm. To trace out one complete rotation around the hexagon, the center of the coin must travel a distance equal to 6 times the circumference of the hexagon, or 6 cm. Adding this to the circumference of the coin gives a total distance of 6 + 3.14 = 9.14 cm.
Deal Guru Oct 16, 2008
10314 posts
Maple
love0715 wrote: hi , wonder if someone can help on this math tutoring Q.

A coin with a diameter 1 cm rolls around the outside of a regular hexagon with a side length of 1 cm (as shown on the attached photo ).

What is the length (in cm) of the path traced out by the centre of the coin after one complete rotation around the hexagon ?

Thanks
TC
OP

You are taking a short cut, in a way it’s cheating!

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[OP]
Sr. Member
Nov 25, 2008
815 posts