Question

If the surface area of two cubes are 1:4 and volume of first cube is 512 m cube. Then what is the volume of second cube?

Answer 1

Let the side of one cube is (a) & the side of second cube is( b)
surface area of one cube is 6a^2
surface area of second cube is 6b^2

vol of first cube =a^3= 512m^3
a^3 = 512
a^3 = 8^3
a=8

now ratio of two cubes is 1:4

6a^2/6b^2=1/4

a^2/b^2=1/4
8^2/ b^2=1/4
64/b^2=1/4
64×4= 1×b^2
256=b^2
16^2=b^2
b=16

vol of second cube =b^3
vol of second cube=16^3
vol of second cube=4096m^3

Answer 2

Let the side of one cube be 'a' and the side of second cube be 'b'.

surface area of first cube = 6a^2

surface area of second cube = 6b^2

volume of first cube = a^3 = 512m^3

a^3 = 512

a^3 = 8^3

a = 8

6a^2 / 6b^2=1/4                (because the ratio between them is 1:4)

a^2 / b^2=1/4

8^2 / b^2=1/4

64 / b^2=1/4

64×4 = 1×b^2                      (via cross multiplication)

256 = b^2

16^2 = b^2

b = 16

volume of second cube =b^3

volume of second cube=16^3

volume of second cube=4096m^3

HOPE IT HELPS YOU!