Let, the radius of earth = R, Therefore, the diameter of earth = 2 R
According to question, diameter of moon = 1/4(2R), So, the radius of moon
= (1/4(2R)/2) = 1/4 R
Now,
Surface area of moon/surface of earth = (4π(1/4R)²)/4π(R)² = (1/16R²)/R² = 1/16
Hence, the ratio of surface areas of moon to earth is 1: 16.