A scale model of a merry-go-round and the actual merry-go-round are similar. a. How many times greater is the base area of the actual merry-go-round than the base area of the scale model? Explain. The ratio of the corresponding lengths is : 1. So, the ratio of the areas is : 1 and the base area of the actual merry-go-round is times greater than the base area of the scale model. b. What is the base area of the actual merry-go-round in square feet? The base area of the actual merry-go-round is square feet.

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]