Question

4. Fine the lateral surface area in sq. cm of a cube its diagonal is √6 cm: *

Answer 1

Hey your answer is :

Let the edge odf the cube be a㎝

length of the diagonal is

3a= 6⇒a= 2㎝

lateral surface area of the cube is 4a2=4×(2)2=4×2=8㎤

Hope it will helpful to you.

please mark it as brainliest answers.

Answer 2

ANSWER:

WE KNOW THAT LATERAL SURFACE AREA OF A CUBE IS $4a^{2}$ where a is the edge of a cube. So, first you have to find the edge of a cube from its diagonal.  So, you know that $\sqrt{l^{2} +b^{2} }$ is the diagonal of a cube. So, :-

$\sqrt{l^{2}+b^{2} } =\sqrt{6}$

=> Since, the length and breadth of a cube are equal. Let the edge be a....

$\sqrt{a^{2}+a^{2} } =\sqrt{6}$

=>$\sqrt{2a^{2} } =\sqrt{6}$

=>2$a^2$=6

=> $a^{2}$=$\frac{6}{2}$

=>$a^{2}$=3

=>a=$\sqrt{3}$

So, now we know the edge of the cube=$\sqrt{3}$

Therefore, lateral surface area=4$a^{2}$

---> 4*$(\sqrt{3})^2$           =>(4*3)$cm^{2}$

ANSWER:  12$cm^{2}$ is the lateral surface area of a cube