The area swept by the minute hand will be?????(read on....)?

Question

The length of a minute hand on a wall clock is 7 cm.The area swept by the minute hand in 30 minutes is how much cm^2?

Answer 1

Hiya...I'm really sorry but I just had to stop and point out the fact that the path of a clock hand will always be a circle irrespective of the shape of the clock and that in half an hour (30 mins) the clock hand will always have rotated exactly 180 degress (mapping a semi-circle). I don't really know how others came to the conclusion that the hands of say, a square-shaped clock, wouldn't travel in a perfect circle. Anyway, the hands are the radius of a circle and so to find the area they pass we must use the formula for the area of a circle, A = π.r². So since in this case our clock's minute hand (ie. our radius) is 7cm and we only want to know the area mapped in 30 mins (ie. area of the semi-circle) then we can halve the formula of a full circle and use:

A = 1/2 π.r²

A = 1/2 π.(7)²

A = 1/2 π x 49

A = (49/2) π

A = 49π/2..........which is your exact area but you can evaluate using a calculator and then rounding.

So the area swept by the minute hand in 30 minutes is 49π/2 cm².

Hope it helps (^_^)

Answer 2

the minute hand goes on circularly

w.r.t assumption 30 minutes swipe means its a half circle so 0.5 *pi*49 cm^2 = 76.96902 cm^2

@indenton  thanx it was juzz a quick thot

Answer 3

you do not have to assume that the clock is circular but you must know that the minute hand will definitely make a circular motion roud your clock.. dun believe, look at your clock now...

anw, after 30 mins, the minute hand would have gone through half a circle in another words, a semicircle

area of a circle = pi x r^2

thus,

area of a semicircle = 1/2 x pi x r^2

where r is 7 , the length of your minute hand

are swept by the minute hand = 1/2 x pi x 7^2

                                            = 76.968955

                                            = 77.0 cm^2 (3 s f)

Answer 4

length of minute hand is 7 so radius is 7

area of circle is 22/7 x r^2

therefore 22/7 x 7x 7=154cm^2

but it is 30 minutes so half  the area =77cm^2

Answer 5

Think of the clock as a circle, with radius of 7cm.  The area swept by the minute hand in 30 minutes is 1/2 the area of the circle because 30 minutes is half of 60.  To find the area of the circle we need this formula:

A=(pi)r^2

Placing the radius in we get 49(pi).  And the answer is half that or A=(49/2)(pi).  

Answer 6

Think of it like a circle.

The area of a circle is

A = π r²

where r is the radius, which in this case is our minute hand.

In 60 minutes we sweep a full circle, in 30 we have a semicircle.

So the total area will be divided by 2....

A = π * (7cm) ²  / 2

A = 49 π  cm²  / 2

A = 24.5 π  cm²

A = 76.97 cm²

So its about 77 cm²