# Volume and Surface Area of Cube

What is Cube?

A cuboid is a cube if its length, breadth and height are equal.

In a cube, all the faces are squares which are equal in area and all the edges are equal. A dice is an example of a cube.

Volume of a Cube (V) = (edge)3 = a3

Total surface Area of a Cube (S) = 6(edge)2 = 6a2

Diagonal a Cube (d) = √3(edge) = √3a

Where a = edge

Problems on Volume and Surface Area of Cube:

1. If the edge of a cube measures 5 cm, find (i) it volume, (ii) its surface area, and (iii) the length of a diagonal.

Solution:

(i) volume = (edge)3

= 53 cm3

= 125 cm3

(ii) Surface area = 6(edge)2

= 6 × 52 cm2

= 6 × 25 cm2

= 150 cm2

(iii) The length of a diagonal = √3(edge)

= √3 × 5 cm.

= 5√3 cm.

2. If the surface area of a cube is 96 cm2, find its volume.

Solution:

Let the edge of the cube be x.

Then, its surface area = 6x2

Therefore, 96 cm2 = 6x2

⟹ x2 = $$\frac{96 cm^{2}}{6}$$

⟹ x2 = 16 cm2

⟹ x = 4 cm.

Therefore, edge = 4 cm.

Therefore, the volume = (edge)3

= 43 cm3

= 64 cm3.

3. A cube of edge 2 cm is divided into cubes of edge 1 cm. How many cubes will be made? Find the total surface area of the smaller cubes.

Solution:

Volume of the bigger cube = (edge)3

= 23 cm3

= 8 cm3.

Volume of each of the smaller cubes = (edge)3

= 13 cm3

= 1 cm3

Therefore, the number of smaller cubes = $$\frac{8 cm^{3}}{1 cm^{3}}$$

= 8

The total surface area of a smaller cube = 6(edge)2

= 6 × 1 cm2

= 6 cm2

Therefore, the total surface area of the eight smaller cubes = 8 × 6 cm= 48 cm2.

## You might like these

• ### Problems on Right Circular Cylinder | Application Problem | Diagram

Problems on right circular cylinder. Here we will learn how to solve different types of problems on right circular cylinder. 1. A solid, metallic, right circular cylindrical block of radius 7 cm and height 8 cm is melted and small cubes of edge 2 cm are made from it.

• ### Hollow Cylinder | Volume |Inner and Outer Curved Surface Area |Diagram

We will discuss here about the volume and surface area of Hollow Cylinder. The figure below shows a hollow cylinder. A cross section of it perpendicular to the length (or height) is the portion bounded by two concentric circles. Here, AB is the outer diameter and CD is the

• ### Right Circular Cylinder | Lateral Surface Area | Curved Surface Area

A cylinder, whose uniform cross section perpendicular to its height (or length) is a circle, is called a right circular cylinder. A right circular cylinder has two plane faces which are circular and curved surface. A right circular cylinder is a solid generated by the

• ### Cylinder | Formule for the Volume and the Surface Area of a Cylinder

A solid with uniform cross section perpendicular to its length (or height) is a cylinder. The cross section may be a circle, a triangle, a square, a rectangle or a polygon. A can, a pencil, a book, a glass prism, etc., are examples of cylinders. Each one of the figures shown

• ### Cross Section | Area and Perimeter of the Uniform Cross Section

The cross section of a solid is a plane section resulting from a cut (real or imaginary) perpendicular to the length (or breadth of height) of the solid. If the shape and size of the cross section is the same at every point along the length (or breadth or height) of the