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A level maths pure

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.
(edited 4 years ago)
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
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
for the trig questions you need to be able to use relationships confidently...

Sin2Θ

cos2Θ

tanΘ

can all be written in other ways.
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
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?
Reply 6
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
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.)
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
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
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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