Question

Find the side of a cube whose surface area is 2400 sq. Cm

Answer 1

Given,

The surface area of the cube = 2400 cm²

To find,

The length of each side of the given cube.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the length of one side of the given cube = a cm

Surface area of the given cube = 6×(side)² = 6a² cm²

According to the data mentioned in the question,

6a² = 2400

a² = 400

a = 20

(This is the final Length of each side of the given cube.)

Hence, the Length of each side of the given cube is 20 cm.

Answer 2

$\sf\underline\red{Given:}$: Total surface area of a cube measures 2400cm².

$\sf\underline\red{To~find}$ : Edge of the cube.

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$\:$

Here,

$\:$

T.S.A of a cube = 2400cm²

$\: \:$

As we know that :

$\: \:$

$\underline{\boxed{\tt\purple{\bigstar \: T.S.A \: of \: a \: cube \: = 6 {a}^{2} }}}$

$\:$

Where

$\:$

"a" denotes edge of the cube.

$\:$

$\boxed {\sf {\green { put~the~value}}}$

$\:$

$\tt:\implies \: 6 {a}^{2} = 2400 \\ \\ \\ \tt:\implies \: {a}^{2} = \frac{2400}{6} \\ \\ \\ \tt:\implies {a}^{2} = \cancel \frac{2400}{6} \\ \\ \\ \tt:\implies \: {a}^{2} = 400 \\ \\ \\ \tt:\implies \: a = \sqrt{400} \\ \\ \\ \tt:\implies \: a = \sqrt{20 \times 20} \\ \\ \\\tt:\implies \: a = \underline{\boxed{\tt\purple{20cm}}}\bigstar \\ \\ \\ \\ \: \: \: \: \tt\therefore{\underline{Hence, \: the \: edge \: of \: the \: cube \: is \: \bold{20cm}.}}$

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More to know :

$\: \:$

• Volume of a cube = a³
• Total surface area of a cube = 6a²
• Curved surface area of a cube = 4a²
• Diagonal of a cube = √3a

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