06. If the ratio of the surface areas of two
cubes is 16:36, then the ratio of their sides
will be :
(1)
4:9
(2)
9:4
3:2
(4) 2:3
Answers
Answer:
(1) 4:9
Step-by-step explanation:
16:36 when divided by 4 give the answer 4:9
If the surface area of cubes are in ratio 16:36 then the ratio of their sides will be 2:3.
Step-by-step explanation:
Let the surface area of two cubes be “S.A.₁” & “S.A.₂” and their sides be denoted as “a₁” & “a₂” respectively.
The ratio of surface areas of two cubes is given = 16:36
The formula for the Surface Area of a cube is given by,
S.A. = 6a²
Therefore,
S.A.₁ / S.A.₂ = 16 / 36
⇒ 6a₁² / 6a₂² = 16/36
⇒ a₁²/a₂² = 16/36
Taking square root on both sides
⇒ a₁/a₂ = 4/6
⇒ a₁/a₂ = 2/3
Thus, the ratio of their sides will be option (4)- 2:3.
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