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.
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
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
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
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.)