Total Surface Area of Cube with Formula and Examples

Total Surface Area of Cube is the sum of the areas of all six equal square faces. For a cube with edge length a, the formula is 6a² square units. This page explains the formula, unit conversion, reverse calculations, common differences between total and lateral surface area, and solved aptitude examples.

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What Is the Total Surface Area of a Cube?

The total surface area of a cube is the area covered by all its six congruent square faces. If the edge of the cube is a, its total surface area is 6a² square units.

Each face has area a × a = a². Since a cube has 6 equal faces, total surface area = a² + a² + a² + a² + a² + a² = 6a². The answer is expressed in square units, such as cm², m² or mm².

Total Surface Area of Cube Video Lessons

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Cube Volume, Surface Area and Diagonal

Learn how to calculate a cube’s volume, surface area, and diagonal using the relevant formulas and understand the relationship between its dimensions and measurements.

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Total Surface Area of Cube Formula & Tricks

Important Formulas

Total surface area
TSA = 6a²

Here, a is the edge length of the cube. The result is measured in square units.

Edge from total surface area
a = √(TSA ÷ 6)

Use this formula when the total surface area is given and the edge length is required.

Area of one face
a² = TSA ÷ 6

Dividing the total surface area by 6 gives the area of one square face.

Lateral surface area
LSA = 4a²

The lateral surface area includes only the four side faces, excluding the top and bottom faces.

Quick Tricks

Square the edge before multiplying by 6

For TSA = 6a², first calculate a² and then multiply by 6. Do not use 6a.

Example: If a = 5 cm, TSA = 6 × 5² = 6 × 25 = 150 cm².
Use the one-face method

Find the area of one square face and multiply it by 6. This avoids forgetting that every face has the same area.

Example: For an edge of 8 m, one face has area 64 m², so TSA = 6 × 64 = 384 m².
Check the unit before squaring

Convert the edge into the required unit before applying the formula because the edge is squared.

Example: An edge of 2 m is 200 cm. TSA = 6 × 200² = 240,000 cm², which is also 24 m².

Total Surface Area of Cube Concepts

Six Equal Square Faces

A cube has six equal square faces, and each face has area a² when its edge is a.

The top, bottom, front, back, left and right faces are all congruent. Therefore, adding the six face areas gives TSA = 6a².

Example: If the edge is 4 cm, the area of one face is 4² = 16 cm², so the area of all six faces is 6 × 16 = 96 cm².

Calculating Total Surface Area from the Edge

To calculate TSA, square the edge length and multiply the result by 6.

Use TSA = 6a². If the edge is given in centimetres, the answer will be in square centimetres; if it is given in metres, the answer will be in square metres.

Example: For a cube of edge 7 cm, TSA = 6 × 7² = 6 × 49 = 294 cm².

Finding the Edge from Total Surface Area

When TSA is known, the edge is a = √(TSA ÷ 6).

First divide the given total surface area by 6 to obtain the area of one face. Then take the positive square root because length cannot be negative.

Example: If TSA = 600 cm², a = √(600 ÷ 6) = √100 = 10 cm.

Total Surface Area Versus Lateral Surface Area

TSA includes all six faces, whereas lateral surface area includes only the four vertical faces.

For edge a, TSA = 6a² and LSA = 4a². The difference is the area of the top and bottom faces, equal to 2a².

Example: For a = 3 m, TSA = 54 m² and LSA = 36 m². Their difference is 18 m², which equals 2 × 3².

Total Surface Area of Cube Visual Guide

Use the diagram or chart below to understand the concept clearly.

Cube with edge length a

Visual guide: Cube with edge length a
Each edge: a Number of faces: 6
A cube has six square faces, each with area a²; their sum is the total surface area 6a².

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Practice Total Surface Area of Cube Questions

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1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

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Quick Revision Notes

Total Surface Area of Cube: Revision Points

Use these formulas and rules for quick revision.

  • A cube has 6 congruent square faces.
  • TSA = 6a², where a is the edge length.
  • The unit of surface area is always a square unit.
  • If TSA is given, edge = √(TSA ÷ 6).
  • Lateral surface area of a cube = 4a².
  • TSA is equal to the sum of lateral surface area and the areas of the top and bottom faces: 4a² + 2a² = 6a².
  • Convert the edge into the required unit before squaring it.

Related Topic Explainers

Area of Square → Perimeter of Square → Area of Rectangle → Perimeter of Rectangle → Area of Triangle → Perimeter of Triangle → Heron's Formula → Area of Triangle Using Two Sides and Included Angle →

Total Surface Area of Cube FAQs

What is the total surface area of a cube with edge 10 cm?

TSA = 6 × 10² = 6 × 100 = 600 cm².

What is the total surface area of a cube with edge 2.5 m?

TSA = 6 × 2.5² = 6 × 6.25 = 37.5 m².

If the total surface area of a cube is 864 cm², what is its edge?

a = √(864 ÷ 6) = √144 = 12 cm.

What happens to the total surface area if the edge of a cube is doubled?

TSA is proportional to a². If the edge becomes 2a, the new TSA is 6(2a)² = 24a², which is four times the original TSA.

What is the difference between total and lateral surface area of a cube?

TSA covers all six faces and equals 6a². Lateral surface area covers four side faces and equals 4a².

What is the total surface area of a cube with edge 30 cm in square metres?

TSA = 6 × 30² = 5,400 cm². Since 10,000 cm² = 1 m², the area is 0.54 m².

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