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Suppose that there are two cubes, having edges $2 cm$ and $4 cm$ , respectively. Find the ratio between the volumes of $V 1$ and $V 2$ cubes.

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1:2

1:8

3:7

5:7

answer is B.

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Detailed Solution

It is given two cubes, having edges

2 cm

and

4 cm

.
Volume of the cube

V = a 3

, where

a

is the side.
Finding the volume of a cube with the edge

2 c m

,
Let the volume of this cube be

V 1

.
Volume of this cube,

V 1 = 2 c m 3 ⇒ V 1 = 8 c m 3

The volume of a cube with the edge

2 c m

is 8

c m 3

.
Finding the volume of a cube with the edge 4

cm

,
Let the volume of this cube be

V 2

.
Volume of this cube,

V 2 = 4 c m 3 ⇒ V 2 = 64 c m 3

The volume of a cube with the edge 4

cm

is 64

c m 3

.
Compare the volumes

V 1

and

V 2

V 1 : V 2 = 8 c m 3 : 64 c m 3 V 1 : V 2 = 1 : 8

Hence, ration is 1:8.
Hence option (2) is correct.

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