Question

If the side of a cube is doubled then find theratio between the volume of the first cube and thenew cube.​

Answer 1

Answer:

1 : 8

Step-by-step explanation:

As per the provided information in the given question, we have :

• There is a cube.
• Its side is doubled.

We are asked to calculate the ratio between the volume of the first cube and the new cube.

$\longrightarrow$ Let us assume the the side of the first cube as "a". Therefore, the side of the new cube becomes "2a" as its side is doubled of the first cube.

★ Volume of the first cube :

$\longrightarrow \sf{\quad { Volume_{(Cube)} = (Side)^3 }}$

Substituting values, side = a.

$\longrightarrow \sf{\quad { Volume_{(Cube)} = (a)^3 }}$

Writing the cube of its side.

$\longrightarrow \quad { \textbf{\textsf{Volume}}_{\textbf{\textsf{(Cube)}}} = \textbf{\textsf{a}}^\textbf{\textsf{3} }}$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

★ Volume of the new cube :

$\longrightarrow \sf{\quad { Volume_{(New \; Cube)} = (Side)^3 }}$

Substituting values, side = 2a.

$\longrightarrow \sf{\quad { Volume_{(New \; Cube)} = (2a)^3 }}$

Writing the cube of its side.

$\longrightarrow \quad { \textbf{\textsf{Volume}}_{\textbf{\textsf{(New \; Cube)}}} = \textbf{\textsf{8a}}^\textbf{\textsf{3}} }$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

★ Ratio between their volumes :

$\longrightarrow \sf{\quad { Ratio_{(Volume)} = \dfrac{Volume_{( Cube)} }{Volume_{(New \; Cube)} } }}$

Substitute the values.

$\longrightarrow \sf{\quad { Ratio_{(Volume)} = \dfrac{a^3 }{8a^3} }}$

Cubes of a will get cancelled.

$\longrightarrow \sf{\quad { Ratio_{(Volume)} = \dfrac{1 }{8} }}$

Henceforth, the ratio can be written as,

$\longrightarrow \quad \underline{\boxed { \textbf{\textsf{Ratio}}_{\textbf{\textsf{(Volumes)}}} =\textbf{\textsf{1 : 8 }}}}$

Therefore,

⠀⠀⠀⠀★ Ratio = 1 : 8

Answer 2

Answer:

The ratio is 1:8

Step-by-step explanation:

Let the initial side of the cube= a units

=> The initial volume = (a units)³= a³ unit³

Now,

The side of the cube is doubled = 2(a units)

= 2a units

The new volume is = (2a unit )³

= 8a³ unit³

Therefore,

The ratio of volume of both the cubes is

= a³ : 8a³

= 1 : 8