Problema Solution
the inside of a track field is consists of a rectangle with two semicircle at both ends. the dimensions of the rectange are 100m by 73m. the track its self is another 10 m around the outside of the interior. if you wanted to replace the surface of a track how much miterial would you need
Answer provided by our tutors
replacing the surface of the track requires replacing an area the size of the entire rectangle and track, minus the area inside of the track
we calculate these areas the area of a circle plus the area of a rectangle, the radius of the circle being half the diameter of the width of the rectangle
the diameter of the outermost circle is 73m + 2*10m = 93m, giving a radius of (93/2)m
the dimensions of the outermost rectangle are length 100m and width 73m + 2*10m = 93m
area of a circle: PI*r^2
area of a rectangle: length * width
total area:
PI*(93/2)^2 + 100*93
we now define the total area inside the track, for which we have a circle of radius (73/2)m and rectangle of 100 x 73 m:
total area:
PI*(73/2)^2 + 100*73
repaving the track will require paving an area that is determined by subtracting the inner area from the outer area:
PI*(93/2)^2 + 100*93 - PI*(73/2)^2 + 100*73 = 4607.52
the surface area of the track itself is approximately 4,608 m^2