Question

If the total surface area of a cube is numerically equal to its volume, then what is the lateral
surface area of the cube in square units?​

Answer 1

Given,

The total surface area of the cube = The volume of the cube

To find,

The lateral surface area of the cube.

Solution,

Let, the length of the each sides of the cube = a unit

[Assume, a as a variable to do the further mathematical calculations.]

Total surface area of the cube = 6a² sq.unit

Volume of the cube = a³ unit³

According to the data mentioned in the question,

6a² = a³

6 = a

Or, a = 6

Length of the side of the cube = 6 unit

Lateral surface area = 4 × (side)² = 4×(6)² = 144 sq.unit

Hence, the lateral surface area of the cube is 144 sq.unit.

Answer 2

FORMULA TO BE IMPLEMENTED

LATERAL SURFACE AREA

The lateral surface of an object is the area of all the sides of the object, excluding the area of its base and top

FORMULA FOR CALCULATING

A cube has 6 sides

So If a is the length of the side of each edge of the cube then lateral surface area

$= \sf{ 4 {a}^{2} } \: \: sq \: \: unit$

GIVEN

The total surface area of a cube is numerically equal to its volume

TO DETERMINE

The lateral surface area of the cube in square units

CALCULATION

Let a is the length of the side of each edge of the cube

Then

$\sf{Volume \: of \: the \: cube \: = {a}^{3} \: } \:$

$\sf{ \: Total \: Surface \: Area \: of \: the \: Cube \: = 6 {a}^{2} \: }$

By the given condition

$\sf{ \: {a}^{3} = 6 {a}^{2} \: }$

$\sf{\implies \: a = 6 \: \: \: \: \: \: \: \: ( \: \because \: a \ne \: 0 \: )\: }$

So the length of the side of each edge of the cube

= 6 unit

Hence the lateral surface area of the cube

$\sf{ \: = 4 \times {(6)}^{2} \: } \: \: sq \: unit$

$\sf{ \: = 4 \times 36 \: } \: \: sq \: unit$

$\sf{ \: = 144 \: } \: \: sq \: unit$

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