For the two similar cuboids A and B,
surface area of A : surface area of B = 16 : 2 then the ratio of their volumes is equal to volume of A : Volume of B = 16√2 : 1.
As given in the question,
Given : Two similar cuboids A and B,
Let x , y , and z be the length , width and height of cuboid A
And l, b, h be the length , width , and height of cuboid B.
As both the cuboids are similar their sides are in proportion.
k is the constant of proportionality then,
x= kl , y = kb, z = kh
Surface area of A : Surface area of B = 16 :2
⇒2k²(lb +bh +hl) : 2(lb +bh +hl) = 16 : 2
⇒k² = 16 :2
⇒k = 4 : √2
Now volume of A : Volume of B
= xyz : lbh
= k³lbh : lbh
= k³
=( 4 : √2)³
=64 : 2√2
= 64√2 : 4
= 16√2 : 1
Therefore, for the two similar cuboids A and B,
surface area of A : surface area of B = 16 : 2 then the ratio of their volumes is equal to volume of A : Volume of B = 16√2 : 1.
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