Mensuration — Sphere, Hemispheres and Rectangular Parallelepiped
What is Mensuration — Sphere, Hemispheres and Rectangular Parallelepiped?
A perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball.
Key formula / rule: Surface Area of Sphere
Key points
- Calculate surface area and volume of spheres and hemispheres.
- Calculate surface area and volume of rectangular parallelepipeds.
- Solve problems involving comparisons and relationships between these shapes.
- Apply mensuration formulas to real-world scenarios.
Common exam trap
Confusing surface area with volume formulas.
Definitions
- Term
Sphere
- Meaning
A perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball.
- Term
Hemisphere
- Meaning
Half of a sphere, typically divided by a plane passing through its center.
- Term
Rectangular Parallelepiped
- Meaning
A solid figure bounded by six rectangular faces; also known as a cuboid.
- Term
Radius
- Meaning
The distance from the center of a sphere or hemisphere to any point on its surface.
- Term
Volume
- Meaning
The amount of three-dimensional space occupied by an object.
- Term
Surface Area
- Meaning
The total area of the outer surfaces of a three-dimensional object.
Learning objectives
Calculate surface area and volume of spheres and hemispheres.
Calculate surface area and volume of rectangular parallelepipeds.
Solve problems involving comparisons and relationships between these shapes.
Apply mensuration formulas to real-world scenarios.
Formulae
- Name
Surface Area of Sphere
- Note
r is the radius of the sphere.
- Expression
4πr²
- Name
Volume of Sphere
- Note
r is the radius of the sphere.
- Expression
(4/3)πr³
- Name
Curved Surface Area of Hemisphere
- Note
r is the radius of the hemisphere.
- Expression
2πr²
- Name
Total Surface Area of Hemisphere
- Note
Includes the base area (πr²). r is the radius.
- Expression
3πr²
- Name
Volume of Hemisphere
- Note
r is the radius of the hemisphere.
- Expression
(2/3)πr³
- Name
Surface Area of Rectangular Parallelepiped (Cuboid)
- Note
l=length, b=breadth, h=height.
- Expression
2(lb + bh + hl)
- Name
Volume of Rectangular Parallelepiped (Cuboid)
- Note
l=length, b=breadth, h=height.
- Expression
lbh
- Name
Diagonal of Rectangular Parallelepiped
- Note
Connects opposite vertices.
- Expression
√(l² + b² + h²)
Prerequisites
Basic geometry concepts (area and perimeter of 2D shapes).
Understanding of π (π) and its approximate value.
Familiarity with basic algebraic manipulation.
Common mistakes
Confusing surface area with volume formulas.
Using diameter instead of radius in formulas.
Forgetting to add the base area for a hemisphere's total surface area.
Incorrectly calculating the diagonal of a cuboid.
Keywords
Sphere
Hemisphere
Rectangular Parallelepiped
Cuboid
Surface Area
Volume
Mensuration
3D Geometry
SSC CGL
Quantitative Aptitude
Practice preview
If the radius of a sphere is equal to the radius of a hemisphere, what is the ratio of the volume of the sphere to the volume of the hemisphere?…
medium
Find the volume of a sphere with a radius of 3 cm. (Use pi = 22/7)…
easy
Calculate the total surface area of a hemisphere with a radius of 7 cm. (Use pi = 22/7)…
easy