Question

The two solids are similar and the ratio between the lengths of their edges is 2:9. What is the ratio of their surface areas?

Answer 1

Hello,

During a dilatation of ratio k (length ratio),
area are multiplied by k² and volume bu k^3.

A)
(2/9)²=4/81 answser A

B) (3/5)²=9/25 Answer D

Answer 2

we know that

If two solids are similar

then

the ratio of their corresponding sides are equal and is called the scale factor

Part 1)

In this problem

$scale\ factor= \frac{2}{9}$

The ratio of their surface areas is equal to the scale factor squared

$scale\ factor^{2}=( \frac{2}{9})^{2} =\frac{4}{81}$

therefore

the answer is the option A

$\frac{4}{81}$

Part 2)

In this problem

$scale\ factor= \frac{3}{5}$

The ratio of their surface areas is equal to the scale factor squared

$scale\ factor^{2}=( \frac{3}{5})^{2} =\frac{9}{25}$

therefore

the answer is the option D

$\frac{9}{25}$