Let the side of a cube be 'a' units.

Then,

(i) The Total Surface Area (T.S.A) = 6a^{2} square units.

(ii) The Lateral Surface Area (L.S.A) = 4a^{2} square units.

(ii) Volume of cube = a^{3} cubic units.

**Example 1 :**

The volume of the cube is 125 dm^{3}. Find its side.

**Solution :**

Volume of cube = 125 dm^{3}

a^{3} = 125

a^{3} = 5^{3}

a = 5 dm

So, side length of cube is 5 dm.

**Example 2 :**

A container is in the shape of a cube of side 20 cm. How much sugar can it hold?

**Solution :**

In order to find the quantity of sugar that the container can hold, we have to find the volume of container.

Side length of cubical container = 20 cm

Volume of container = a^{3}

= (20)^{3}

= 8000 cm^{3}

**Example 3 :**

A cubical tank can hold 64,000 litres of water. Find the length of the side of the tank.

**Solution :**

Let a be the side of the cubical tank. Volume of the tank is 27,000 litres. So,

V = a^{3} = (27000/1000)

a^{3} = 27

a = ∛27

a = 3 m

**Example 4 :**

Three metallic cubes of side 3 cm, 4 cm and 5 cm respectively are melted and are recast into a single cube. Find the total surface area of the new cube.

**Solution :**

Side length of 1^{st} cube = 3 cm

Side length of 2^{nd} cube = 4 cm

Side length of 3^{rd} cube = 5 cm

Volume of 1^{st}, 2^{nd} and 3^{rd} cube = 3^{3} + 4^{3} + 5^{3}

= 27 + 64 + 125

= 216

a^{3} = 216

a^{3} = 6^{3}

a = 6 cm

Total surface area of new cube = 6a^{2}

= 6(6)^{2}

= 6(36)

= 216 cm^{2}

So, total surface area of new cube 216 cm^{2}

**Example 5 :**

Find the L.S.A, T.S.A and volume of a cube of side 5 cm.

**Solution :**

Lateral surface area (L.S.A) = 4a^{2}

= 4(52 ) = 100 sq. cm

Total surface area (T.S.A) = 6a^{2}

= 6 (5^{2} )

= 150 sq. cm

Volume of cube = a^{3}

= 5^{3}

= 125 cm^{3}

**Example 6 :**

Find the length of the side of a cube whose total surface area is 216 square cm.

**Solution :**

Let a be the side of the cube.

Given that T.S.A = 216 sq. cm

6a^{2} = 216

a^{2} = 216/6

a^{2} = 36

a = √36

a = 6 cm

**Example 7 :**

A cube has a total surface area of 384 sq. cm. Find its volume.

**Solution :**

Let a be the side of the cube. Given that T.S.A = 384 sq. cm

6a^{2} = 384

a^{2} = 384/6

a^{2} = 64

a = √64 = 8 cm

So, volume is

= a^{3}

= 8^{3}

= 512 cm^{3}

**Example 8 :**

If the lateral surface area of a cube is 900 cm^{2}, find the length of its side.

**Solution :**

Lateral surface area of cube = 4a^{2}

4a^{2 }= 900

a^{2 }= 900/4

a^{2 }= 225

a = √225

a = 15 cm

So, the side of cube is 15 cm.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**