# A level maths pureWatch

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#1
Hey stuck on some questions would appreciate some help .im on a roll today with questions .could someone explain working out to part b on first attachment.
Last edited by abbeygyal23; 1 month ago
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1 month ago
#2
(Original post by abbeygyal23)
Hey stuck on some questions would appreciate some help .im on a roll today with questions .could someone explain working out to part b on first attachment.
you just gotta split the shape up into its components , so first you have 2 rectangles of dimensions( the sides of the diagram) 10 x 20 , so 10x20x 2= 400 the bit without the pi in what you need to reach. then you have x2 the the area of the sector which is ( ((pi/4)/2pi) x pi x 20squared) ( x 2 cuz 2 of them on the botttom and top) which gives you 100 pi , then you also have the the curved edge of this "slice of cake" , you get this from arc length x height , so (2x pi x 20 x ((pi/4)/2pi)) x 10 = 50 pi which you add to the previous areas to get 400 + 150 pi as required
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1 month ago
#3
(Original post by burntcherrio)
you just gotta split the shape up into its components , so first you have 2 rectangles of dimensions( the sides of the diagram) 10 x 20 , so 10x20x 2= 400 the bit without the pi in what you need to reach. then you have x2 the the area of the sector which is ( ((pi/4)/2pi) x pi x 20squared) ( x 2 cuz 2 of them on the botttom and top) which gives you 100 pi , then you also have the the curved edge of this "slice of cake" , you get this from arc length x height , so (2x pi x 20 x ((pi/4)/2pi)) x 10 = 50 pi which you add to the previous areas to get 400 + 150 pi as required
( ((pi/4)/2pi) refers to the fraction of pi/4 of the whole circle of 2 pi
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1 month ago
#4
for the trig questions you need to be able to use relationships confidently...

Sin2Θ

cos2Θ

tanΘ

can all be written in other ways.
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#5
(Original post by burntcherrio)
you just gotta split the shape up into its components , so first you have 2 rectangles of dimensions( the sides of the diagram) 10 x 20 , so 10x20x 2= 400 the bit without the pi in what you need to reach. then you have x2 the the area of the sector which is ( ((pi/4)/2pi) x pi x 20squared) ( x 2 cuz 2 of them on the botttom and top) which gives you 100 pi , then you also have the the curved edge of this "slice of cake" , you get this from arc length x height , so (2x pi x 20 x ((pi/4)/2pi)) x 10 = 50 pi which you add to the previous areas to get 400 + 150 pi as required
Hi thank you!!!!I understand the area of the rectangle however I am still confused after that .Why is it (pi/4)/2pi)x pi x20squared.The underlined bit is the bit I don't really get. With the curved edge is this not part of the area of 100pi?Sorry I'm just confused
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#6
(Original post by burntcherrio)
( ((pi/4)/2pi) refers to the fraction of pi/4 of the whole circle of 2 pi
Oh okay I understand the 2PI bit now but after this?
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1 month ago
#7
(Original post by abbeygyal23)
Oh okay I understand the 2PI bit now but after this?
2x area of rectangle = 400
2x area of sector = 2*50*pi=100pi
Area formed by arc = length of arc * height = 20*pi/4 *10 = 50pi
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1 month ago
#8
(Original post by abbeygyal23)
Oh okay I understand the 2PI bit now but after this?
after that the pi x 20 squared is for the area of (the fraction pi/4 of the whole of 2 pi) of the circle (the sector), so pi x radiussquared (x the fraction) and the radius is 20 so the area of the sector, is (pi/4)/2pi)x pi x20squared. (the top and bottom of the diagram u drew.)
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1 month ago
#9
(Original post by vbzl)
2x area of rectangle = 400
2x area of sector = 2*50*pi=100pi
Area formed by arc = length of arc * height = 20*pi/4 *10 = 50pi
this exactly
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1 month ago
#10
(Original post by vbzl)
2x area of rectangle = 400
2x area of sector = 2*50*pi=100pi
Area formed by arc = length of arc * height = 20*pi/4 *10 = 50pi
here is a ms paint diagram, that should help visualize this
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#11
(Original post by burntcherrio)
here is a ms paint diagram, that should help visualize this
Yes this really helped thank you So
Much!!!!! I am a visual person so this really helped with clarity !!!!!!
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