Question

3. Find the surface area and the diagonal of a cube, whose edge is 18 cm.

Answer 1

Given :

Edge of Cube = 18 cm

To Find :

Surface Area and Diagonal of Cube.

Formula To Find :

$\rm \: Surface \: Area \:of \: Cube = 6 \: {a}^{2}$

$\rm \: Diagonal \: of \: Cube \: = \sqrt{3} \: a$

Where, a = Edge of Cube

Solution :

Surface Area Of Cube :

$\dashrightarrow \sf \: A = 6 \: {a}^{2}$

$\dashrightarrow \sf A= 6 \times {18}^{2}$

$\dashrightarrow \sf \: A = 6 \times 18 \times 18$

$\sf \dashrightarrow \: A = 6 \times 324$

$\sf \dashrightarrow \: A = 1944$

A = 1944 cm^2

Diagonal Of Cube :

$\dashrightarrow \sf D = \sqrt{3} \: a$

$\sf\dashrightarrow \: D = \sqrt{3} \times 18$

$\sf\dashrightarrow \: D = 1.73 \times 18$

$\dashrightarrow \sf D = 31.14$

D = 31.14 cm

$\therefore \sf \: Surface \: Area \: of \: Cube \: = 1944 \: cm^² \\ \sf And \: Diagonal \: of \: Cube \: = 31.14 \: cm$

Answer 2

$\blue\bigstar$ Answer:

• Total Surface Area = 1944 cm²
• Diagonal = 31.176 cm

$\orange\bigstar$Given:

• Edge of the cube = 18cm

$\green\bigstar$To find:

• Surface Area of the cubeDiagonal of the cube

$\purple\bigstar$Solution:

Edge of the cube = 18 cm

Formula for Total Surface Area of the cube = 6a²

(Where "a" is the "edge")

So, $\sf \: Total \: Surface \: Area \: = \: 6 {a}^{2}$

$\sf\implies \: Total \: Surface \: Area \: = \: 6 \: \times \: 18cm \: \times \: 18cm \: \\ ( \: \tt \: where \: "a" \: = \: edge \: \: of \: the \: cube )$

$\sf \implies \: Total \: Surface \: Area \: = \boxed{ \: \sf1944 \: \sf{cm}^{2} }$

$\sf\therefore \: The \: Total \: Surface \: Area \: of \: the \: cube \: is \: 1944 {cm}^{2}$

Now, The Diagonal of a cube = √3a

(where "a" = edge of the cube )

So,$\sf Diagonal \: of \: the \: cube \: = \: \sqrt{3} \: a \:$

$\sf \: \implies \: Diagonal \: of \: the \: cube \: = \: \sqrt{3} \times \: 18 \: cm$

$\sf \: \implies \: Diagonal \: of \: the \: cube \: = \: 1.732 \: \times \: 18$

$\sf \: \implies \: Diagonal \: of \: the \: cube \: = \: \boxed{ \sf \: 31.176 \: cm}$

$\sf \: \therefore \: The \: Diagonal \: of \: the \: cube \: is \: 31.176 \: cm \: (approx.)$

$\pink\bigstar$Concepts Used:

• Total Surface Area of a cube = 6a²
• Diagonal of a cube = √3 a

(where, a = edge of the cube)

$\red\bigstar$ Additional Information :

• Lateral Surface Area of a cube = 4a² (where a = edge of the cube)
• Total Surface Area of a Cuboid = 2(lb + bh + hl)
• Lateral Surface Area of the Cuboid = 2(lh + bh)
• $\sf Diagonal \: of \: a \: cuboid \: = \: \sqrt{ {l}^{2} \: + \: {b}^{2} \: + \: {h}^{2} }$

( where l = Length of the Cuboid, b = Breath of a Cuboid, h = height of the Cuboid)