Question

19. The areas of corresponding faces of two similar hexagonal prisms are 25 cm² and 121 cm². What is the ratios of the corresponding sides lengths? of the perimeter? of the volumes?

Answer 1

I) 5:11

ii) 5:11

iii) 125:1331

Step-by-step explanation

Let the side lengths be in the ratio:

x:y

This implies that the area will be in the ratio:

`\frac{ {x}^(2) }{ {y}^(2) } = (25)/(121)`

Take positive square root.

`(x)/(y) = \sqrt{ (25)/(121) }`

`(x)/(y) = (5)/(11)`

Hence the sides are in the ratio:

x:y=5:11

The perimeter of the smaller hexagon is 6×5=30

The perimeter of the larger hexagon is 6×11=66

The ratio of the perimeter is

30:66=5:11

The volume will be in the ratio

5³:11³

125:1331