Fun problem. Let's just look at the side of the roll, it's a circle and we'll assume the wallpaper is rolled all the way up to the center.
The circle has area [tex]\pi (20/2)^2 = 100 \pi [/tex]
When we use 1/4 of the roll we'll have 3/4 left. The material is proportional to the area of the circle we've been looking at, so we seek the radius r where
[tex]\pi r^2 = \frac 3 4 (100 \pi) = 75 \pi[/tex]
[tex]r = \sqrt{75}=5 \sqrt{3} [/tex]
The diameter is twice that:
Answer [tex] 10 \sqrt{3} [/tex]
Choice b.
