Mensuration (3D) Formulas Tips And Tricks

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Mensuration (3D) Formulas Tips And Tricks

It is very important to have an understanding of Different Formulas of quadrilaterals and circle for you to comfortably attempt Advanced Maths questions which covers a major portion of Quant Section of Competitive Exams. Here we are providing you formulas and shortcuts on how to solve mensuration questions.

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)

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 )

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

Prism

• Volume = Base area x height

• Lateral Surface area = perimeter of the base x height

Pyramid

• 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 whole surface of a right pyramid = area of the lateral faces + area of the base.