Sport track covering

Question

At the edge of the sports field as shown in the picture, there is a running track area with a width of 6m. How much paving is needed when one cubic meter can cover 18 m^2? The area of the field is 1514m2

Answer 1

corrected so straight lengths are 60m not 70m

if the field area is 1514m² then each end is made of half circle radius 10m.

and track straight section field area is 60*20 added to the field area of the each end.

outside radius is 16 of each half circle end

area of field plus track at either end =(1/2)π16²=402.13m²

area of field at either end =(1/2)π10²=157m²

track area either end=245.13m²

times 2 =490.26m²

straight sections for track have area =2*60*6=720m²

total track area=1210.26m²

divided by 18 = 67.23 cubic meters of paving material.

rounded up = 68 cubic meters

Answer 2

Draw and label a diagram!

The striaght sides of the track are 60 x 6 m.

80 minus the two 10 radius semicircles.

1) Straight track is 720 m²

Each section of curved tack is (0.5)(16²π - 10²π)

There are two (2)(0.5)(16²π - 10²π)

(16² - 10²)π

156π m²

2) Curved track is 490 m²

Can you add both areas, divide by 18 and answer?