
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?
Answer
518.1k+ 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
Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Chemistry: Engaging Questions & Answers for Success

Trending doubts
10 examples of friction in our daily life

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

How many valence electrons does nitrogen have class 11 chemistry CBSE
