Question

A scale model of a merry-go-round and the actual merry-go-round are similar.

1. How many times greater is the base of the actual merry-go-round than the base area of the scale model? Explain.
2. What is the base area of the actual merry-go-round in square feet?

Answer 1

Step 1: Find the relation between the base area of actual merry-go-round and the base area of the scale model.

Given,

From given figure, we can say that

Radius of model merry-go-round is $6\mathrm{inches}$

Radius of actual merry-go-round is $10\mathrm{ft}=120\mathrm{inches}$

Since, we know that when two figures are similar then,

$\Rightarrow \frac{AreaoffigureA}{AreaoffigureB}=\frac{{(sidelengthoffigureA)}^2}{{(sidelengthoffigureB)}^2}$

So, for relation of actual and model merry-go-round will be

$\Rightarrow \frac{AreaoffigureA}{AreaoffigureB}=\frac{{120}^2}{6^2}=400$

Step 2:Find the base area of the actual merry-go-round.

Radius of model merry-go-round is $6\mathrm{inches}$

Radius of actual merry-go-round is $10\mathrm{ft}=120\mathrm{inches}$

Area of base of model merry-go-round is $450sq.inches$

Since, for similar figure we can say that

$$\begin{gathered} \Rightarrow \frac{Areaofbaseofactualmerry}{Areaofbaseofmodelmerry}=\frac{{(radiusofactualmerry)}^2}{(radiusofmodelmerry)2} \\ \Rightarrow \frac{Areaofbaseofactualmerry}{450}=\frac{{120}^2}{6^2} \\ \Rightarrow Areaofbaseofactualmerry=400\times 450=180000sq.inches=1250sq.ft \end{gathered}$$

Step 3: Final answer.

Hence, base area of the actual merry-go-round is $400$ times greater than the base area of the model merry-go-round and area of base of actual merry-go-round is $1250sq.ft$.