Let the diameter of the earth be 'd'. then the diameter of the moon will be 'd/4'
radius of the earth = d/2
radius of the moon= 1/2 x d/4 = d/8
surface area of the moon = 4 x pi x (d/8)^2
surface area of the earth = 4 x pi x (d/2)^2
required ratio= 4 pi(d/8)^2 ÷ 4 pi(d/2)^2
∴the ratio between their surface areas is 1:16