LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

VOLUME & SURFACE AREA OF CUBE

__CUBE –__

**All its 12 edges are equal in length. So, a cube is a cuboid in which length = breadth = height**

**The volume of a cube will be measured by the cube of the length of its side. Denoting the volume of a cube by V and its length L.**

**So, V = Lᶟ, L = 3√ V**

**The surface area of a cube is the sum of the areas of its six square faces or 6 X (length of an edge)². Denoting the surface area by S,**

**S = 6L² and L = √(S/6)**

**The area of the four walls (lateral surface area) = 4 X (length of an edge)² = 4L² **

**Since a cube is a special cuboid in which l = b = h = L, **

**the length of a diagonal of a cube = √ l² + b² + h² **

** = √ L² + L² + L² **

** = √3L² = √3 L**

**so, the length of a diagonal = √3 L **

**Example.) The length of a diagonal of a cube is 15√3 cm. find the (a) length of an edge of the cube, (b) the volume of a cube, and (c) the surface area of the cube.**

**Ans.) let the length of each edge of a cube is = a cm**

**As per the rules length of the diagonal = √3a cm**

**So, as per the given condition- √3 a = 15√3, **

** a = 15 cm **

**so, the length of the edge of the cube is 15 cm…………………..(a)**

**the desired volume of the cube is = (length of a side)ᶟ **

** = (15 cm)ᶟ = 3375 cmᶟ ………………..(b)**

**the surface area of the cube = 6 X (length of a side)² **

** = 6 X (15)² = 1350 cm² ……………..(c)**