Surface Area of 3D Shapes

Surface Area of 3D Shapes

Definition

Surface area is the total area of the surface of a 3D shape.

Formulae

• Cube: 6s^2 (where s is the side length)
• Rectangular Prism: 2(lw + lh + wh) (where l, w, and h are the length, width, and height respectively)
• Cylinder: 2πr(h + r) (where r is the radius and h is the height)
• Sphere: 4πr^2 (where r is the radius)
• Cone: πr(r + l) (where r is the radius and l is the slant height)
• Pyramid: B + (1/2)pl (where B is the base area, p is the perimeter of the base, and l is the slant height)

Key Concepts

• Surface area is measured in square units (e.g. cm^2, m^2)
• Surface area includes the area of all faces of the 3D shape
• Surface area is used in real-world applications such as architecture, engineering, and design

Tips and Tricks

• Make sure to use the correct formula for each type of 3D shape
• Convert between units if necessary (e.g. from meters to centimeters)
• Break down complex shapes into simpler shapes to calculate surface area

Surface Area of 3D Shapes

Definition

• Surface area is the total area of the surface of a 3D shape.

Formulae

• Cube: 6s^2, where s is the side length
• Rectangular Prism: 2(lw + lh + wh), where l, w, and h are the length, width, and height respectively
• Cylinder: 2πr(h + r), where r is the radius and h is the height
• Sphere: 4πr^2, where r is the radius
• Cone: πr(r + l), where r is the radius and l is the slant height
• Pyramid: B + (1/2)pl, where B is the base area, p is the perimeter of the base, and l is the slant height

Key Concepts

• Surface area is measured in square units, such as cm^2 or m^2
• Surface area includes the area of all faces of the 3D shape
• Surface area is used in real-world applications, including architecture, engineering, and design

Tips and Tricks

• Use the correct formula for each type of 3D shape
• Convert between units if necessary, such as from meters to centimeters
• Break down complex shapes into simpler shapes to calculate surface area