Respuesta :
The area ratio is the square of the linear dimension ratio. So if the merry-go-round base is circular, the area contains the square of the radius. If a polygon, the base can be divided into triangles. The area of each triangle involves the product of the base length and the height, so since both have the same change of length, the product will square the scaling ratio.
Let’s say the ratio of corresponding lengths is x:1 then the ratio of the base areas is x²:1.
The question doesn’t provide any figures.
Let’s put some in as an example. Let the actual merry-go-round be circular with a diameter of 20 feet, while the model is one foot in diameter. So the ratio of the actual ride and it’s model is 20:1. The area of the base of the actual ride is 100π sq ft. The area of the base of the model is π/4 sq ft. We expect the ratio of these areas to be 20²=400. 100π/(π/4)=400.
Let’s say the ratio of corresponding lengths is x:1 then the ratio of the base areas is x²:1.
The question doesn’t provide any figures.
Let’s put some in as an example. Let the actual merry-go-round be circular with a diameter of 20 feet, while the model is one foot in diameter. So the ratio of the actual ride and it’s model is 20:1. The area of the base of the actual ride is 100π sq ft. The area of the base of the model is π/4 sq ft. We expect the ratio of these areas to be 20²=400. 100π/(π/4)=400.
