Question

if the surface area of a cubical block is 96 cm^2.


find the length of its edge

find volume

give direct answer

no Explanation

Answer 1

Answer:

Surface area of a cubical block is given by the formula :

Let the side of the cube be a

S.A = 6 a²

Given :

S.A = 96 cm² .

⇒ 6 a² = 96 cm²

⇒ a² = 96 cm²/6

⇒ a² = 16 cm²

⇒ a = 4 cm

The length of the edge of the cube is 4 cm .

Volume of cube = a³ .

⇒ Volume = ( 4 cm )³

⇒ Volume = 64 cm³ .

The side is 4 cm and volume is 64 cm³ .

Step-by-step explanation:

Volume of the body = area of cross section × height .

Since all the sides of a cube are equal :

Volume = length of one side × side²

⇒ Volume = side³ .

Surface area is the area of all the 6 surfaces of a cube where each surface has 2 equal sides a and is a square .

Hence surface area = 6 a² .

Answer 2

$\mathfrak{Answer:}$

Edge = 4 cm & Volume = 64 cm³.

$\mathfrak{Step-by-Step\;Explanation:}$

$\underline{\bold{Given\;in\;the\;Question:}}$

• Surface area of a cubical block = 96 cm².

Let the length of its edge be x cm.

$\bigstar\quad\textbf{We know that : \boxed{\bold{Surface\;Area\;of\;cube=6\times (side)^2}}}\\\\\\\mathfrak{According\;to\;Question:}\\\\\\\implies\tt{6x^2=96}\\\\\\\implies\tt{x^2=\dfrac{96}{6}}$

$\implies\tt{x^2=16}\\\\\\\implies\tt{x=\pm 4.}\\\\\\\therefore\quad\textbf{Possible value of x = 4 cm.}\\\\\\\bigstar\quad\textbf{We also know that :\boxed{\bold{Volume\;of\;cube=(side)^3}}}$

$\tt{=(4\;cm)^3}\\\\\\\tt{=64\;cm^3.}\\\\\\\boxed{\boxed{\bold{Length\;of\;its\;edge=4\;cm\quad\&\quad Volume=64\;cm^3.}}}$