Answer

Verified

388.8k+ views

Hint: Let any variable be the side of the cube and the surface area and volume of the cube is 6 times side square and side cube respectively so use these concepts to reach the solution of the question.

Complete step-by-step answer:

As we know that the cube has 6 sides and each side represents the square.

And the area of square is $ = {\left( {{\text{side}}} \right)^2}$

Let the side length of the cube be a unit.

So the surface area (S.A) of the cube is $ = 6{a^2}$ sq. unit

$ \Rightarrow S.A = 6{a^2}$ sq. unit ………………….. (1)

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

$ \Rightarrow V = {a^3}$ unit cube………………………… (2)

Now it is given that the edge of the cube is doubled.

So now the edge of the cube becomes 2a.

So the new surface area ($S.{A_1}$) of the cube is $ = 6{\left( {2a} \right)^2} = 6\left( {4{a^2}}

\right) = 24{a^2}$ sq. unit.

$ \Rightarrow S.{A_1} = 4\left( {6{a^2}} \right)$

Now from equation (1) we have,

$ \Rightarrow S.{A_1} = 4\left( {S.A} \right)$

So the new surface area of the cube is four times the old surface area.

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

$ \Rightarrow {V_1} = 8{a^3}$

Now from equation (2) we have,

$ \Rightarrow {V_1} = 8\left( V \right)$

So, the new volume of the cube is eight times the old volume.

So, this is the required answer.

Note: Whenever we face such types of problem the key concept is formula of surface area and volume of cube which is stated above then make the side double as given in problem statement and calculate new surface area and volume of the cube as above then convert new surface area and volume in terms of old surface area and volume of the cube as above so, doing this we can easily calculate how much times the surface area and volume of the cube is increased if the edge of the cube is doubled.

Complete step-by-step answer:

As we know that the cube has 6 sides and each side represents the square.

And the area of square is $ = {\left( {{\text{side}}} \right)^2}$

Let the side length of the cube be a unit.

So the surface area (S.A) of the cube is $ = 6{a^2}$ sq. unit

$ \Rightarrow S.A = 6{a^2}$ sq. unit ………………….. (1)

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

$ \Rightarrow V = {a^3}$ unit cube………………………… (2)

Now it is given that the edge of the cube is doubled.

So now the edge of the cube becomes 2a.

So the new surface area ($S.{A_1}$) of the cube is $ = 6{\left( {2a} \right)^2} = 6\left( {4{a^2}}

\right) = 24{a^2}$ sq. unit.

$ \Rightarrow S.{A_1} = 4\left( {6{a^2}} \right)$

Now from equation (1) we have,

$ \Rightarrow S.{A_1} = 4\left( {S.A} \right)$

So the new surface area of the cube is four times the old surface area.

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

$ \Rightarrow {V_1} = 8{a^3}$

Now from equation (2) we have,

$ \Rightarrow {V_1} = 8\left( V \right)$

So, the new volume of the cube is eight times the old volume.

So, this is the required answer.

Note: Whenever we face such types of problem the key concept is formula of surface area and volume of cube which is stated above then make the side double as given in problem statement and calculate new surface area and volume of the cube as above then convert new surface area and volume in terms of old surface area and volume of the cube as above so, doing this we can easily calculate how much times the surface area and volume of the cube is increased if the edge of the cube is doubled.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

What is the past participle of wear Is it worn or class 10 english CBSE

What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE

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

The coefficient of xn 2 in the polynomial left x 1 class 9 maths CBSE

How do you know if an equation is linear or nonlin class 10 maths CBSE