MATH SOLVE

5 months ago

Q:
# 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

Accepted Solution

A:

Answer: 16: 49Step-by-step explanation:If two shapes are similar , then the following condition holds(i) the ratio of their sides are equal(ii) If [tex]l_{1}[/tex] is the length of the first one and [tex]l_{2}[/tex] is the length of the second one then:[tex]\frac{A_{1} }{A_{2} }[/tex] = [tex]\frac{(L_{1} )^{2} }{L_{2}) ^{2} }[/tex]Where A stands for the area(iii) Β [tex]\frac{V_{1} }{V_{2} }[/tex] = [tex]\frac{(L_{1} )^{3} }{L_{2}) ^{3} }[/tex]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:[tex]\frac{A_{1} }{A_{2} }[/tex] = [tex]\frac{4^{2} }{7^{2} }[/tex][tex]\frac{A_{1} }{A_{2} }[/tex] = 16/49Therefore the ratio of their surface area is 16: 49