Question

the volume of two cubes are in the ratio 27 isto 64 .find the ratio of their surface areas​

Answer 1

Answer:

9 : 16

Step-by-step explanation:

Given-----> Volume of two cubes are in the ratio 27:64 .

To find-----> Ratio of their surface areas

Solution-----> Let edges of cubes be x and y .

Now we know that ,

Volume of cube = edge³

Surface area of cube = 6 ( edge )²

Volume of first cube = edge³

V₁ = x³

Volume of second cube = y³

V₂ = y³

ATQ, Ratio of volume of cubes = 27 : 64

=> V₁ : V₂ = 27 : 64

=> V₁ : V₂ = 27 : 64

=> V₁ / V₂ = 27 / 64

=> x³ / y³ = 3³/ 4³

=> ( x / y )³ = ( 3 / 4 )³

=> x / y = 3 / 4

We know that,

Surface area of cube = 6 ( edge )²

Surface area of first cube = 6 x²

=> S₁ = 6x²

Surfae area of second cube = 6y²

=> S₂ = 6y²

S₁ / S₂ = 6x² / 6y²

= x² / y²

= ( x / y )²

= ( 3 / 4 )²

= 9 / 16

=> S₁ : S₂ = 9 : 16