The width of an arch is 1.4 m and the semicircle at the top begins at a height of 1.9 m. What is the minimum amount of material in square metres needed to cover the whole arch so you cannot see through it?

Respuesta :

Answer:

The minimum amount of material in m^2 that will be needed to cover the whole arc will be 3.43 m^2

Step-by-step explanation:

This arc can be divide into two shape; a semi circle with a diameter of 1.9 m, and a rectangle with a width 1.9 m and a height of 1.4 m

For the semicircle, the area = [tex]\frac{\pi d^{2} }{4}[/tex] Ă· 2

where d is the diameter

==> [tex]\frac{3.142 * 1.4^{2} }{4}[/tex] Ă· 2

==> 1.539 Ă· 2 = 0.7695 m^2

For the rectangle, area = width x height

==> 1.4 x 1.9 = 2.66 m^2

Total area = 0.7695 + 2.66 = 3.43 m^2

This is the minimum amount of material that will be needed to cover the whole arc.