Table of contents  
Cube and Cuboid  
Net of a Cube  
Formulas of a Cube  
Total Surface of a Cube  
Volume of a Cube  
Cuboid  
Net of a Cuboid  
Formulas of a Cuboid  
Solved Examples – Cube and Cuboid Formula 
In our daily life, we see many objects like notebooks, matchboxes, instrumental geometry boxes, cones, cricket balls, cylinders, etc. These are all threedimensional objects (solid shapes). All these objects occupy some shape and have three dimensions Length, Breadth, Height, or Depth.
Moreover, we often find some shapes with two or more identical (congruent) faces. For example, the Cube has squared faces on each side, and the Cuboid has rectangular faces on each side. A Cube and Cuboid is a threedimensional shape with six faces, eight vertices, and twelve edges. The main distinction is that a cube has the same length, width, and height on all sides, whereas a cuboid has varied length, breadth, and height. Both shapes appear to be nearly the same, however, they have different properties.
A square is a twodimensional figure with two dimensions length and breadth, while a cube is a threedimensional figure with three dimensions length, breadth, and height. The side faces of a cube are formed by squares. Also knowing the cube and cuboid formula will enable students to know the difference between cube and cuboid easily.
Common examples of Cube in real life are square ice cubes, dice, sugar cubes, Rubik’s cube etc.
A cube shape is like that of perfect square. Cube is a threedimensional boxlike figure represented in the threedimensional plane. Cube has 6 squareshaped equal faces. Each face meets another face at 90^{o} each. Three sides of the cube meet at the same vertex.
In the given figure, faces, edges and vertices of a cube have been shown. 8 corners of the cube are its vertices. The line segments forming the cube are its 12 edges. The six square faces forming the cube are its 6 faces.
The net of a solid is a diagram drawn on paper which when cut and folded along the lines can be used to construct a solid shape. Net of a Cube is a twodimensional shape that can be folded into a three dimensional figure is a Cube.
A Cube consists of 6 square faces, 12 edges, and 8 vertices. When the square faces of a cube are separated at the edges and laid out flat, they make a twodimensional figure called a net.
Lateral Surface Area of a Cube:
Consider a Cube of edge length ‘a′ , then, the area of each face of a square = a^{2}
So, the Lateral Surface Area of a Cube = Sum of the area of all 4 side faces Lateral Surface Area(LSA) = 4a^{2} square units
We know the cube consists of 6 square faces. Let us consider if each side of a cube is a , then the total surface area of the Cube is = 6a^{2}.
Total Surface Area (TSA) = 6a^{2} square units
The volume of a cube can be found by multiplying the edge length three times. If each edge length is “a” , then the Volume of a Cube is a^{3}.
V = a^{3} cubic units
A rectangle is a twodimensional figure with two dimensions length and breadth, while a cuboid is a threedimensional figure with three dimensions length, breadth, and height. The side faces of a cuboid are formed by rectangles.
Common examples of cuboid in real life are bricks, the lunch box, notebook, and Geometry instrumental box.
Cuboid is a threedimensional boxlike figure represented in the threedimensional plane. Cuboid has 6 rectangularshaped equal faces. Each face meets another face at 90^{o} each. Three sides of the cuboid meet at the same vertex.
A cuboid consists of 6 rectangular faces, 12 edges, and 8 vertices. When the rectangular faces of a cuboid are separated at the edges and laid out flat, they make a twodimensional figure called a net of a Cuboid. A cuboid shape is like that of a rectangular shoe box.
We know the cuboid consists of 6 rectangular faces.
Total Surface Area (TSA) =2(lb+bh+hl) square units
Where, l= length, b= breadth, h= height
Volume of a cuboid is V = length × breadth × height
V = (l × b × h) Cubic units
Q1: Find the volume of the cube whose each edge is 5cm.
Ans: From the given edge a = 5cm
Volume of a Cube is a^{3}.
V = a^{3} cubic units
⇒ V = 5^{3}
⇒ V = 125cm^{3}
Hence, the volume of a Cube is 125cm^{3}.
Q2: Find the volume of the cuboid whose dimensions are length = 6m , breadth = 6m , height = 6m.
Ans: Given: = 6m,breadth = 4m, height = 3m
Volume of a Cuboid =length × breadth × height
⇒ Volume of a Cuboid = 6 × 4 × 3
⇒ V = 72m^{3}
Hence, the volume of a Cuboid is 72m^{3}.
Q3: Find the surface area of a cube whose edge is 6cm.
Ans: From the given = 6cm
The total surface area of the Cube is 6a^{2}.
Total Surface Area (TSA)=6×(6)^{2} square units
= 6 × 36 = 216cm^{2}
Hence, the surface area of a Cube is 216cm^{2}.
Q4: What is the lateral surface area of a cube of edge 10cm
Ans: From the given = 10cm
The Lateral Surface Area of a Cube = Sum of area of all 4 side faces
Lateral Surface Area(LSA) =4a^{2} square units
⇒ LSA = 4 × 10^{2}
⇒ LSA = 4 × 100
⇒ LSA = 400cm^{2}
Hence, the obtained lateral surface area of a cube is 400cm^{2}.
Q5: A cuboidshaped wooden block has 5cm length, 4cm breadth and 5cm height. Find the total surface area of a Cuboid.
Ans: Given: Length 5cm , Breadth 4cm , Height 5cm
Total Surface Area (TSA) = 2(lb+bh+hl) square units
⇒ TSA = 2(5×4+4×1+1×5)
⇒ TSA = 2(20+4+5)
⇒ TSA = 2(29)
⇒ TSA = 58cm^{2}
Hence, the obtained total surface area of a Cuboid is 58cm^{2}.
131 videos171 docs117 tests

1. What is the net of a cube? 
2. What are the formulas for a cube? 
3. What is the net of a cuboid? 
4. What are the formulas for a cuboid? 
5. Can you provide an example of how to use the cube and cuboid formulas? 
131 videos171 docs117 tests


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