If the radii of umbra and penumbra cast by an object on a wall are of the ratio 2:6, what is the area of the penumbra ring around the umbra of the latter’s radius is 40 cms?

• let the radius of umbra and penumbra are 2k and 6k.
  Then as given radius of umbra=40cm
  so 2k=40
  k=20
  radius of penumbra=20*6=120
  area of penumbra ring around the umbra=area of penumbra-area of umbra
  22/7*[(120)^2-(40)^2]
  =40288.57cm^2
• 13 years agoHelpfull: Yes(10) No(0)
• here u need to find the area b/w two concentric circles...
  radius of umbra and penumbra arin ratio 2:6.
  given radius of umbra=40cm
  therefore 2:6=40:x (2/6=40/x)
  x=radius of penumbra=120
  use formula 22/7*(R^2-r^2)
  ans=40288.57cm^2
• 13 years agoHelpfull: Yes(2) No(0)