Question

The total surface area of a cube is 150 cm”. Find the perimeter of any one of its
faces.​

Answer 1

Given:

• A cube is given to us .
• Total Surface Area if a cube is 150cm²

To Find:

• Perimeter of any one of its side.

Concept Used:

• We will make use of the formula for finding total surface area of a cube .
• Secondly we will use the formula to find the perimeter of any one of its surface.

Solution:

Here its given that TSA of the cube is 150cm².

So , Formula for TSA of cube is :

$\large{\underline{\boxed{\red{\sf{TSA_{cube}=6a^{2}}}}}}$

where

• a is the measurement of its side .

Using above formula we have ,

$\sf{\implies 6a^{2}=150cm^{2}}$

$\sf{\implies a^{2}=\dfrac{150cm^{2}}{6}}$

$\sf{\implies a^{2}=25cm^{2}}$

$\sf{\implies a =\sqrt{25cm^{2}}}$

${\underline{\red{\sf{\leadsto a=5cm}}}}$

Therefore measure of side of cube is 5cm.

Therefore measure of side of cube is 5cm.Now ,Formula for Perimeter of one side :

$\large{\underline{\boxed{\red{\sf{Perimeter_{cube}=4\times side}}}}}$

=$\sf{4\times 5cm}$

=${\underline{\red{\sf{20cm}}}}$

Therefore perimeter of one of its side is 20cm.