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

ANSWER

I) 5:11

ii) 5:11

iii) 125:1331

EXPLANATION

Let the side lengths be in the ratio:

x:y

This implies that the area will be in the ratio:

$\frac{ {x}^{2} }{ {y}^{2} } = \frac{25}{121}$

Take positive square root.

$\frac{x}{y} = \sqrt{ \frac{25}{121} }$

$\frac{x}{y} = \frac{5}{11}$

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