Important Mensuration (3D) Formulas
Cube
- s = side
- Volume: V = s^3
- Lateral surface area = 4a2
- Surface Area: S = 6s^2
- Diagonal (d) = s√3
Cuboid
- Volume of cuboid: length x breadth x width
- Total surface area = 2 ( lb + bh + hl)
Right Circular Cylinder
- Volume of Cylinder = π r^2 h
- Lateral Surface Area (LSA or CSA) = 2π r h
- Total Surface Area = TSA = 2 π r (r + h)
Hollow-Cylinder
r1 = outer radius
r2 = inner radius
Right Circular Cone
- l^2 = r^2 + h^2
- Volume of cone = 1/3 π r^2 h
- Curved surface area: CSA= π r l
- Total surface area = TSA = πr(r + l )
Important relation between radius, height and slant height of similar cone.
Frustum of a Cone
- r = top radius, R = base radius,
- h = height, s = slant height
- Volume: V = π/ 3 (r^2 + rR + R^2)h
- Surface Area: S = πs(R + r) + πr^2 + πR^2
Sphere
- r = radius
- Volume: V = 4/3 πr^3
- Surface Area: S = 4π^2
Hemisphere
- Volume-Hemisphere = 2/3 π r^3
- Curved surface area(CSA) = 2 π r^2
- Total surface area = TSA = 3 π r^2
Quarter-Sphere
Let 'r' is the radius of given diagram. You have to imagine this diagram, this is 1/4th part of Sphere.
Prism
- Volume = Base area x height
- Lateral Surface area = perimeter of the base x height
Pyramid
- The volume of a right pyramid = (1/3) × area of the base × height.
- Area of the lateral faces of a right pyramid = (1/2) × perimeter of the base x slant height.
- Area of the whole surface of a right pyramid = area of the lateral faces + area of the base.
Important:
1.From a solid cylinder no. of the maximum solid cone of same height and radius as cylinder are 3.
2. From a solid sphere, no. of a maximum solid cone having height and radius equal can be made are 4.
3. From a solid hemisphere, no. of a maximum solid cone having height and radius equal can be made are 2.
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