Question

12) The side of a cube is 4m.If it is doubled how many times will be the volume of
the new cube as compared with the original eube?​

Answer 1

Step-by-step explanation:

volume of cube = a³

but side = a = 4 m

volume of cube = 4³

= 64

if we double the side of cube then, side = 2a = 8m

the volume of the new cube

= 8³

= 512

Answer 2

${\underline{\underline{\pmb{\sf{\maltese\:Question:}}}}}$

• The side of a cube is 4 m. If it is doubled, how many times will be the volume of the new cube, as compared with the original cube?

${\underline{\underline{\pmb{\sf{\maltese\:Required\:Answer:}}}}}$

• The volume of new cube is 8 times more as compared to the original cube.

${\underline{\underline{\pmb{\sf{\maltese\:Given:}}}}}$

• Side of the cube = 4m

${\underline{\underline{\pmb{\sf{\maltese\:To\:Find:}}}}}$

• Number of times the volume of new cube as compared to the volume of original cube, if the side of the cube gets doubled.

${\underline{\underline{\pmb{\sf{\maltese\:Formula\:used:}}}}}$

To solve this question, we will be using volume of cube formula:

$\bigstar\underline{\boxed{\pink{\sf{Volume\:of\:cube = \bf(Side)^3}}}}$

${\underline{\underline{\pmb{\sf{\maltese\:Concept\:involved:}}}}}$

In this problem, side of the original cube is given. We will be using the formula of volume of cube to find the volume of original cube. Then, we will double the side of the cube as per the question and find the volume of the doubled side, which is nothing but the volume of new cube. At last, we divide the volume of new cube by the volume of the actual cube and compare them.

${\underline{\underline{\pmb{\sf{\maltese\:Solution:}}}}}$

We know that the side of the original cube is 4m. Let us find the volume of original cube:

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

$\sf{\longrightarrow Volume_{(Original\:Cube)} = (4)^3}$

$\longrightarrow\boxed{\red{\sf{Volume_{(Original\:Cube)} = \bf 64m^3}}}$

Now, let us find the volume of new cube. Before finding it, double the side of the cube.

$\sf{\longrightarrow Side_{(New\:cube)} = Side_{(Original\:cube)} \times 2}$

$\sf{\longrightarrow Side_{(New\:cube)} = 4 \times 2}$

$\blue{\sf{\longrightarrow Side_{(New\:cube)} = 8m}}$

Hence, we have found the side of new cube. Now, let us find the volume of the new cube:

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

$\sf{\longrightarrow Volume_{(New\:Cube)} = (8)^3}$

$\longrightarrow\boxed{\orange{\sf{Volume_{(New\:Cube)} = \bf 512m^3}}}$

Let us divide volume of new cube by volume of original cube to compare them.

$\bf{\longrightarrow \dfrac{Volume_{(New\:Cube)}}{Volume_{(Original\:Cube)}}}$

$\bf{\longrightarrow \dfrac{512}{64}}$

$\longrightarrow{\green{\sf{8}}}$

${\underline{\underline{\pmb{\sf{\maltese Conclusion:}}}}}$

Hence, the volume of new cube is 8 times greater than that of its original cube.