Question

find the total surface area of a cube whose volume is 125cm³​

Answer 1

Question:

Find the total surface area of a cube whose volume is 125cm³.

To find:

• Surface area of cube

Given :

• Volume of cube = 125

Solution:

We know:

$\bigstar \boxed{ \rm{}Surface \: Area \: of \: cube = 6 {(side)}^{2} }$

So as we can see here we need value of side so first let's find side of cube

Formula of Volume of cube:

$\bigstar \boxed{ \rm{Volume \: of \: cube = ( {side)}^{3} }}$

By using this formula we can find value of side

$\leadsto\sf{}Volume \: of \: cube = ( {side)}^{3}$

$\leadsto\sf{}125= ( {side)}^{3}$

$\leadsto\sf{}side = \sqrt[3] {125}$

$\leadsto\sf{}side = {125}^{ \frac{1}{3} }$

$\leadsto\sf{}side = { \{5 \times 5 \times 5 \}}^{ \frac{1}{3} }$

$\leadsto\sf{}side = { \{5 {}^{3} \}}^{ \frac{1}{3} }$

$\leadsto\sf{}side = { \{5\}}^{ \frac{3}{3} }$

$\leadsto\sf{}side = { \{5\}}^{ \cancel \frac{3}{3} }$

$\leadsto \underline{ \boxed{\sf{}side =5 \: cm}}$

$\therefore \: \underline{ \sf{}length \: of \: side \: = \: 5 \: cm}$

Now Let's find surface area by using formula mentioned above:

$\leadsto\sf{}Surface \: Area \: of \: cube = 6 {(side)}^{2}$

$\leadsto\sf{}Surface \: Area \: of \: cube = 6 { \times 5}^{2}$

$\leadsto\sf{}Surface \: Area \: of \: cube = 6 { \times 5\times 5}$

$\leadsto\sf{}Surface \: Area \: of \: cube = 6 { \times 25}$

$\leadsto \underline{ \boxed{\sf{}Surface \: Area \: of \: cube = 150 \: cm}}$

$\therefore \: \underline{ \sf{}Surface \: area \: of \: cube = \: 150 \: cm}$

Answer 2

Question:

• Find the total surface area of a cube whose volume is 125cm³.

To find:

• Surface area of cube

Given :

• Volume of cube = 125

Solution:

• We know:

$\bigstar \boxed{ \rm{}Surface \: Area \: of \: cube = 6 {(side)}^{2} }$

So as we can see here we need value of side so first let's find side of cube

Formula of Volume of cube:

$\bigstar \boxed{ \rm{Volume \: of \: cube = ( {side)}^{3} }}$

By using this formula we can find value of side

$\leadsto\sf{}Volume \: of \: cube = ( {side)}^{3}$

$\leadsto\sf{}125= ( {side)}^{3}$

$\leadsto\sf{}side = \sqrt[3] {125}$

$\leadsto\sf{}side = {125}^{ \frac{1}{3} }$

$\leadsto\sf{}side = { \{5 \times 5 \times 5 \}}^{ \frac{1}{3} }$

$\leadsto\sf{}side = { \{5 {}^{3} \}}^{ \frac{1}{3} }$

$\leadsto\sf{}side = { \{5\}}^{ \frac{3}{3} }$

$\leadsto\sf{}side = { \{5\}}^{ \cancel \frac{3}{3} }$

$\leadsto \underline{ \boxed{\sf{}side =5 \: cm}}$

$\therefore \: \underline{ \sf{}length \: of \: side \: = \: 5 \: cm}$

Now Let's find surface area by using formula mentioned above:

$\leadsto\sf{}Surface \: Area \: of \: cube = 6 {(side)}^{2}$

$\leadsto\sf{}Surface \: Area \: of \: cube = 6 { \times 5}^{2}$

$\leadsto\sf{}Surface \: Area \: of \: cube = 6 { \times 5\times 5}$

$\leadsto\sf{}Surface \: Area \: of \: cube = 6 { \times 25}$

$\leadsto \underline{ \boxed{\sf{}Surface \: Area \: of \: cube = 150 \: cm}}$

$\therefore \: \underline{ \sf{}Surface \: area \: of \: cube = \: 150 \: cm}$