Part A:
Given that the base radius of the scale model is 6 in while the base radius of the actual merry-go-round is 10 ft = 10 x 12 = 120 in.
The ratio of the radius of the actual merry-go-round to the radius of the scale model of the merry-go-round is given by 120 : 6 = 20 : 1.
The ratio of the area of the actual merry-go-round to the area of
the scale model of the merry-go-round is given by [tex]20^2 : 1^2=400:1[/tex].
Therefore, the base area of the actual merry-go-round is 400 times greater than the base area of the scale model.
Part B:
The base area of the merry-go-round is in the shape of a circle.
The area of a circle is given by [tex]\pi r^2[/tex]
Given that the radius of the actual merry-go-round is 10 ft.
Therefore, the base area of the actual merry-go-round is given by [tex]\pi\times10^2=100\pi \ ft^2[/tex]
