How far does a clock hand travel if it is a certain length?

[Myboi]

I have a question (sorry I've never used this site before, excuse my bad title) (I'm also in year 8, so this question is probably too easy to be posted here)

The minute hand of a clock is 2cm long. How much area does it cover in 45 minutes?

Could someone please explain how to figure out this question for me please?

 

[Deleted member 4993]

I have a question (sorry I've never used this site before, excuse my bad title) (I'm also in year 8, so this question is probably too easy to be posted here)

The minute hand of a clock is 2cm long. How much area does it cover in 45 minutes?

Could someone please explain how to figure out this question for me please?

Please follow the rules of posting at this forum, enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/

Please share your work/thoughts and context of the problem (what is the subject topic?) - so that we know where to begin to help you.

The clock hand/s sweeps a circular area.

So the area it cover in 60 minutes is the whole circle of radius 2 cm. How much area is that?

Now calculate how much area would it cover in 45 minutes? use ratio.

 

[HallsofIvy]

Think of the minute hand, in one hour, moving through a circle with radius equal to the length of the minute hand. What is the circumference of that circle? Now what fraction of an hour is 45 minutes?

 

[Deleted member 4993]

Think of the minute hand, in one hour, moving through a circle with radius equal to the length of the minute hand. What is the circumference of that circle? Now what fraction of an hour is 45 minutes?

The question is, however,:

How much area does it cover in 45 minutes?

 

[Myboi]

The clock hand/s sweeps a circular area.

So the area it cover in 60 minutes is the whole circle of radius 2 cm. How much area is that?

Now calculate how much area would it cover in 45 minutes? use ratio.

So, The clock hand travels around 45 minutes out of 60 minutes, which is 3/4. So to find out the area that the hand travels, we find out the area of the whole circle and then divide by four. The minute hand only travels around 3 out of the quarters, so the area it covers is 9.42cm². Right?

 

[Deleted member 4993]

Correct....

area of the circle = pi * 2² = 4 * pi

3/4 of the area of the circle = 3/4 * 4 * pi = 3 * 3.1415 = 9.42 cm²