Expert answers to "What is the ratio of the surface areas..."

High School
Geometry
High school geometry
Similarity

CMIIh

Answered question

2021-01-22

What is the ratio of the surface areas of similar solids whose similarity ratio is 4 : 7?

Answer & Explanation

Derrick

Skilled2021-01-23Added 94 answers

Step 1
Given Similarity $r a t i o = \frac{4}{7}$
Similarity ratio : if two solids are similar then. their corresponding sides are all proportional.
Step 2
$R a t i o o f s u r f a c e a r e a s = {(s i m i l a r i t y r a t i o)}^{2}$
Surface area is two dimensional property.
$∴ R a t i o o f s u r f a c e a r e a s = {(s i m i l a r i t y r a t i o)}^{2}$
$= {(\frac{4}{7})}^{2} = \frac{16}{49}$
$∴ R a t i o o f s u r f a c e a r e a s = \frac{16}{49}$

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