Question

There are 7 similarly shaped figures in a set. The largest figure is 7 inches tall. Each of the other figures is 1 inch shorter than the next larger figure. The surface area of the largest figure is 588 in. squared. What is the surface area of the smallest figure?

Answer 1

The first thing we must do for this case is to find the scale factor based on the dimensions of the figures.
 The largest figure is 7 inches tall. Each of the other figures is 1 inch shorter than the next larger figure.
 We have then that the smallest figure has a height of 1 inch.
 The scale factor is:
 k = (smallest figure) / (largest figure) = 1/7
 k = 1/7
 The surface area of the smaller figure is:
 A = k ^ 2 * (A ')
 Where
 A ': surface area of the largest figure.
 Substituting:
 A = (1/7) ^ 2 * (588)
 A = 12 in ^ 2
 Answer:
 The surface area of the smallest figure is:
 A = 12 in ^ 2