Question

if the volume of two cube's arein the ratio 8:1,then the ratio of their edges is
a.8:1
b.2:1
c.3:4
d.1:1​

Answer 1

Given,

Volume of two cube's are in the ratio of 8 : 1

To find :

Ratio of edges of the cubes

Solution :

Let the edge of bigger cube be x and smaller cube be y

We know that

Volume of a cube = ( Edge of a cube )³ cu.units

Volume of bigger cube = x³ cu.units

Volume of smaller cube = y³ cu.units

Ratio of volumes = 8 : 1

⇒ x³ / y³ = 8 / 1

⇒ ( x / y )³ = 8 / 1

⇒ x / y = ³√ ( 8 / 1 )

⇒ x / y = ³√8 / ³√1

⇒ x / y = 2 / 1

⇒ x : y = 2 : 1

Therefore the ratio of the edges is ( b ) 2 : 1.

Answer 2

Given: The volumes of two cubes are in the ratio 8:1.

To find: The ratio of their edges.

Answer:

Let the edge of one cube be 'a' and the other be 'b'.

Now, volume of a cube = side³.

$\implies\ \sf Volume_{cube\ 1}\ =\ a^3\ and\ Volume_{cube\ 2}\ =\ b^3.$

$\sf \dfrac{Volume_{cube\ 1}}{Volume_{cube\ 2}}\ =\ \dfrac{8}{1}\\\\\\\dfrac{a^3}{b^3}\ =\ \dfrac{8}{1}\\\\\\\bigg(\dfrac{a}{b}\bigg)^3\ =\ \dfrac{8}{1}\\\\\\\dfrac{a}{b}\ =\ \sqrt[3]{\bigg(\dfrac{8}{1}\bigg)} \\\\\\\dfrac{a}{b}\ =\ \dfrac{2}{1}$

Therefore, ratio of their edges = 2:1 ⇒ Option (B).