If each edge of a cube is doubled,
$\left( i \right)$how many times will its surface area increase?
$\left( {ii} \right)$how many times will its volume increase?
Last updated date: 23rd Mar 2023
•
Total views: 311.4k
•
Views today: 8.88k
Answer
311.4k+ views
Hint: Surface area of a cube is $A = 6{l^2}$ and volume is $V = {l^3}$ where $l$ is the side of a cube.
According to the question,
First let’s assume that the side of a cube is $l$
Then the surface area of cube will be $ = 6 \times l \times l$
$\left( i \right)$Initial surface area$ = 6 \times l \times l$
Now as per the question if each edge is doubled then,
New surface area$ = 6 \times 2l \times 2l$$ = 4 \times \left( {6 \times l \times l} \right)$ that means New surface area is equal to four times of initial surface area.
So, the new surface area will be increased by $4$ times.
$\left( {ii} \right)$Initial volume$ = l \times l \times l$
Now as per the question if each edge is doubled then,
Final volume$ = 2l \times 2l \times 2l = 8 \times l \times l \times l$ that means New final volume is equal to eight times of initial volume.
So, volume will be increased by $8$ times.
Note- This type of question is very easy to do. Always approach by assuming the side of the cube as in our solution we assumed the side of the cube to be $l$. After this just follow the steps and find the surface area and volume of the cube. Remember all the formulas related to cube
According to the question,
First let’s assume that the side of a cube is $l$
Then the surface area of cube will be $ = 6 \times l \times l$
$\left( i \right)$Initial surface area$ = 6 \times l \times l$
Now as per the question if each edge is doubled then,
New surface area$ = 6 \times 2l \times 2l$$ = 4 \times \left( {6 \times l \times l} \right)$ that means New surface area is equal to four times of initial surface area.
So, the new surface area will be increased by $4$ times.
$\left( {ii} \right)$Initial volume$ = l \times l \times l$
Now as per the question if each edge is doubled then,
Final volume$ = 2l \times 2l \times 2l = 8 \times l \times l \times l$ that means New final volume is equal to eight times of initial volume.
So, volume will be increased by $8$ times.
Note- This type of question is very easy to do. Always approach by assuming the side of the cube as in our solution we assumed the side of the cube to be $l$. After this just follow the steps and find the surface area and volume of the cube. Remember all the formulas related to cube
Recently Updated Pages
Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry 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 the 6 fundamental rights of India and explain in detail

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

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE
