2. INDEX
Sl No Content Page
Number
1 Prism 1
2 Types of Prism 1
3 Characteristics of Prisms 2
4 Making Prism 3
5 Surface Area of Rectangular
Prism
4
6 Surface Area of Square Prism 5
7 Surface Area of Cube 6
8 Volume of rectangular Prism 7
9 Exercise 8
3. CHAPTER I
PRISMS
A solid object with two identical ends and flat sides:
• The sides are parallelograms (4-sided shape with opposites sides parallel)
• The cross section is the same all along its length
The sides of prism are called its faces. The rectangular faces are called
the lateral faces and the other two are called bases.
TYPES OF PRISMS
1. Triangular Prism
2. Rectangular Prism
3. Square Prism
4. Cube
4. Characteristics of Prisms
Prisms have 2 end faces
End faces are the bases
Bases have same shape and size (Congruent)
All lateral faces are rectangular in shape ( Except in circular prisms)
Naming the prisms based on shapes of bases
The number of edges of each base and the number of lateral edges are
equal, the total number of edges will be a multiple of 3.
The number of vertices of each base is the same, the total number of
vertices will be an even number.
The relationship among the total number of faces, vertices and edges is
F + V – E = 2
5. Making Prisms
We can cut a rectangular prism made of paper and then spread it out flat like
this:
So, in reverse, by cutting out such a figure in paper and by folding and pasting it
at the appropriate places, we can make a rectangular prism.
6. Surface Area of Rectangular Prism
The sum of the areas of all faces of a prism is called its surface area.
The base of rectangular prism is in the shape of rectangle.
A rectangular prism has 6 lateral faces and 2 base faces
A rectangular faces are the lateral faces.
Surface Area = 2*(1*b+b*h+l*h)
Where
l = Length
b = Breadth
h = Height
7. Surface Area of Square Prism
The base of square prism is in the shape of square
Square prism has 6 lateral faces and 2 base faces
Rectangular faces are lateral faces
Square faces are base faces or end faces
Surface Area = 2*a*(a+2*h)
Where
a = side of the square
h = height
8. Surface Area of Cube
The base faces are square, the face are also square
Surface area of cube = 6 * a2
9. Volume of Rectangular Prism
Where, l = Length
b = Breadth
h = Height
Volume of Rectangular Prism = l * b * h
10. Exercise
1. Find the surface area of rectangular Prism of length 24cm, breadth 15cm,
and height 3cm?
2. Find surface area of square prism having a side 5cm, and height 15cm ?
3. What is the surface area of side 5cm?
4. The pillars on the veranda of a school are square prisms of base length 20 cm
and height 2.25m. There are 60 such pillars. What is the total cost of painting
them all, at 250 Rupees per square meter. ?
5. There are 2 water tanks atop a building, each of height 2m. One is rectangular
prism of base lengths 8m and 2 m and other is square prism of base length
4m. What is the volume of each? What is the cost of painting the outer
surface of each tank, at 250 Rupees per square meter? Which costs less?
6. The length, breadth and height of a rectangular prism are 10, 6 and 8cm.
Narrow metal strips are to be fixed along all its edges. What is the total
length of metal strips needed?
