Geometry Formulas

Surface Area of Prisms

• Formula: 2 × (lw + lh + wh) where l = length, w = width, and h = height
• Includes the area of the two bases and the lateral surface area
• Lateral surface area is the area of the sides of the prism

Surface Area of Spheres

• Formula: 4 × π × r^2 where r = radius
• The surface area of a sphere is equal to four times the area of the great circle
• A great circle is a circle that divides the sphere into two equal parts

Surface Area of Cones

• Formula: π × r × (r + l) where r = radius and l = slant height
• Includes the area of the circular base and the lateral surface area
• Lateral surface area is the area of the curved side of the cone

Volume of Cylinders

• Formula: π × r^2 × h where r = radius and h = height
• The volume of a cylinder is equal to the area of the circular base times the height

Volume of Pyramids

• Formula: (1/3) × Bh where B = base area and h = height
• The volume of a pyramid is equal to one-third the base area times the height

Surface Area of Pyramids

• Formula: B + (n × s × l) where B = base area, n = number of sides, s = slant height, and l = length of one side
• Includes the area of the base and the lateral surface area
• Lateral surface area is the area of the triangular sides of the pyramid