Mensuration — Right Prism, Right Circular Cone and Right Circular Cylinder
What is Mensuration — Right Prism, Right Circular Cone and Right Circular Cylinder?
A prism whose lateral faces are rectangles and are perpendicular to the bases.
Key formula / rule: Volume of Right Prism
Key points
- To understand the properties of right prisms, right circular cylinders, and right circular cones.
- To derive and apply formulas for surface area and volume of these shapes.
- To solve problems involving combinations of these shapes.
- To interpret and solve word problems related to mensuration.
Common exam trap
Confusing slant height with perpendicular height in cones.
Definitions
- Term
Right Prism
- Meaning
A prism whose lateral faces are rectangles and are perpendicular to the bases.
- Term
Right Circular Cylinder
- Meaning
A cylinder whose bases are circles and whose axis is perpendicular to the bases.
- Term
Right Circular Cone
- Meaning
A cone whose base is a circle and whose axis is perpendicular to the base, connecting the apex to the center of the base.
- Term
Slant Height (l)
- Meaning
The distance from the apex to any point on the circumference of the base of a cone.
- Term
Lateral Surface Area (LSA)
- Meaning
The sum of the areas of the lateral faces of a solid.
- Term
Total Surface Area (TSA)
- Meaning
The sum of the areas of all faces of a solid, including the bases.
- Term
Volume (V)
- Meaning
The amount of space occupied by a three-dimensional object.
Learning objectives
To understand the properties of right prisms, right circular cylinders, and right circular cones.
To derive and apply formulas for surface area and volume of these shapes.
To solve problems involving combinations of these shapes.
To interpret and solve word problems related to mensuration.
Formulae
- Name
Volume of Right Prism
- Note
Ab is the area of the base, h is the height.
- Expression
V = Ab × h
- Name
Lateral Surface Area of Right Prism
- Note
Pb is the perimeter of the base, h is the height.
- Expression
LSA = Pb × h
- Name
Volume of Right Circular Cylinder
- Note
r is the radius of the base, h is the height.
- Expression
V = πr²h
- Name
Lateral Surface Area of Right Circular Cylinder
- Note
r is the radius of the base, h is the height.
- Expression
LSA = 2πrh
- Name
Total Surface Area of Right Circular Cylinder
- Note
r is the radius of the base, h is the height.
- Expression
TSA = 2πr(r+h)
- Name
Volume of Right Circular Cone
- Note
r is the radius of the base, h is the perpendicular height.
- Expression
V = (1/3)πr²h
- Name
Lateral Surface Area of Right Circular Cone
- Note
r is the radius of the base, l is the slant height.
- Expression
LSA = πrl
- Name
Total Surface Area of Right Circular Cone
- Note
r is the radius of the base, l is the slant height.
- Expression
TSA = πr(r+l)
- Name
Slant Height of Cone
- Note
r is the radius of the base, h is the perpendicular height.
- Expression
l = √(r² + h²)
Prerequisites
Basic geometry concepts (area and perimeter of polygons and circles).
Understanding of 2D shapes.
Basic arithmetic and algebraic skills.
Familiarity with π (π).
Common mistakes
Confusing slant height with perpendicular height in cones.
Using incorrect formulas for LSA/TSA/Volume.
Not considering the units of measurement (e.g., cm vs. m).
Calculation errors in square roots or π values.
Forgetting to add the area of the bases for Total Surface Area.
Keywords
Mensuration
Right Prism
Right Circular Cylinder
Right Circular Cone
Surface Area
Volume
Slant Height
Height
Radius
Base Area
Perimeter
Practice preview
Find the volume of a right circular cylinder with radius 7 cm and height 10 cm. (Use pi = 22/7)…
easy
A right prism has a triangular base whose sides are 3 cm, 4 cm, and 5 cm. If the height of the prism is 10 cm, what is its volume?…
easy
A right circular cylinder and a right circular cone have the same radius and the same height. If the volume of the cylinder is 900 cm^3, what is the volume of the cone?…
medium