# If the edges of the cube are halved, then its volume become is:

$

{\text{a}}{\text{. 4 times}} \\

{\text{b}}{\text{. 8 times}} \\

{\text{c}}{\text{. }}\dfrac{1}{8}{\text{times}} \\

{\text{d}}{\text{. }}\dfrac{1}{2}{\text{times}} \\

$

Last updated date: 17th Mar 2023

•

Total views: 308.4k

•

Views today: 2.87k

Answer

Verified

308.4k+ views

Hint: - Volume of cube $ = {\left( {{\text{Side}}} \right)^3}$

Let, the side of the cube is $a$

As we know the volume$\left( V \right)$ of the cube is $ = {\left( {{\text{Side}}} \right)^3}$

$ \Rightarrow V = {a^3}..........\left( 1 \right)$

Now, if the edges of the cube is halved therefore new edge becomes,

${a_1} = \dfrac{a}{2}$

So, the volume$\left( {{V_1}} \right)$of the new cube is $ = {\left( {\dfrac{a}{2}} \right)^3} = \dfrac{{{a^3}}}{8}$

$\left( {{V_1}} \right) = \dfrac{{{a^3}}}{8}..........\left( 2 \right)$

So, from equation (1) and (2)

${V_1} = \dfrac{V}{8}$

So, the new volume becomes $\dfrac{1}{8}$times the previous volume.

Hence option (c) is correct.

Note: - In such types of questions the key concept we have to remember is that always remember the formula of volume of the cube, then calculate the new volume of the cube according to given condition, then we will get the required answer.

Let, the side of the cube is $a$

As we know the volume$\left( V \right)$ of the cube is $ = {\left( {{\text{Side}}} \right)^3}$

$ \Rightarrow V = {a^3}..........\left( 1 \right)$

Now, if the edges of the cube is halved therefore new edge becomes,

${a_1} = \dfrac{a}{2}$

So, the volume$\left( {{V_1}} \right)$of the new cube is $ = {\left( {\dfrac{a}{2}} \right)^3} = \dfrac{{{a^3}}}{8}$

$\left( {{V_1}} \right) = \dfrac{{{a^3}}}{8}..........\left( 2 \right)$

So, from equation (1) and (2)

${V_1} = \dfrac{V}{8}$

So, the new volume becomes $\dfrac{1}{8}$times the previous volume.

Hence option (c) is correct.

Note: - In such types of questions the key concept we have to remember is that always remember the formula of volume of the cube, then calculate the new volume of the cube according to given condition, then we will get the required answer.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India