Question

if the volume of two cube are in the ratio of 27:64. find the ratio of their edge​

Answer 1

Question:

If the volume of two cubes are in the ratio of 27:64. find the ratio of their edge.

Answer:

3:4

Note:

The volume of cube of edge a is given as ;

V = a^3

Solution:

It is given that;

The volume of two cubes are in ratio 27:64.

Let the edge of first cube be a1 and volume be V1 ,

Thus,

V1 = (a1)^3

Also,

Let the edge of second cube be a2 and volume be V2 ,

Thus,

V1 = (a1)^3

Now,

According to the question,

=> V1 : V2 = 27 : 64

=> V1 / V2 = 27/64

=> (a1)^3 / (a2)^3 = 3^3 / 4^3

=> (a1 / a2)^3 = (3/4)^3

=> a1 / a2 = 3/4

=> a1 : a2 = 3:4

Hence,

The ratio of edges of the two cubes is 3:4 .

Answer 2

Answer:

Let two edges be a and b

volume ratio = 27/64

27 = 3^3 , 64 = 4^3

As volume of cube = (edge)^3

So, a^3/b^3 = 3^3/4^3

a/b = 3/4

So, ratio of edges 3:4

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