The two solids below are similar, and the ratio between the lengths of their edges 4:7 what is the ratio of their surface areas

Question

asked Dec 21, 2020 116k views

2 Answers

RatajS · Answer 1 · 2020-12-27T00:02:19+0000

Answer: 16: 49

Explanation:

If two shapes are similar , then the following condition holds

(i) the ratio of their sides are equal

(ii) If
l_(1) is the length of the first one and
l_(2) is the length of the second one then:

(A_(1) )/(A_(2) ) =
((L_(1) )^(2) )/(L_(2)) ^(2) )

Where A stands for the area

(iii)
(V_(1) )/(V_(2) ) =
((L_(1) )^(3) )/(L_(2)) ^(3) )

Following theses conditions , the ratio of the lengths of their edges is given to be 4 : 7 , then the ratio of their surface area implies:

(A_(1) )/(A_(2) ) =
(4^(2) )/(7^(2) )

(A_(1) )/(A_(2) ) = 16/49

Therefore the ratio of their surface area is 16: 49