Volume and Surface Area of 3D Figures

SAT Math · Axiom Academy

Volume & Surface Area of 3D Figures Learn the formulas for calculating volumes and surface areas of cylinders, cones, spheres, and rectangular prisms. In this lesson, you'll master: Volume and surface area formulas for cylinders, cones, spheres, and rectangular prisms How to apply these formulas to real SAT-style problems Multi-step problems involving 3D figures When to use each formula and how to identify which 3D shape is described A rectangular prism has length ( l ), width ( w ), and height ( h ). A box has dimensions 5 cm × 3 cm × 2 cm. Find its volume and surface area. = 2(15 + 10 + 6) = 2(31) = 62 square cm A cylinder has a circular base and height ( h ). Let r be the radius of the base. A cylinder has radius 4 cm and height 10 cm. Find its volume and surface area. A cone has a circular base with radius r and height h . A cone has radius 3 cm and height 8 cm. Find its volume. A sphere is a 3D ball with radius r . A sphere has radius 5 cm. Find its volume and surface area. Which holds more water: a cylinder with radius 2 cm and height 10 cm, or a sphere with radius 3 cm? , so the cylinder holds more water. A rectangular prism has dimensions 6 cm × 4 cm × 3 cm. What is its volume? A cylinder has radius 6 cm and height 15 cm. What is its surface area? Learn the 4 main 3D shape formulas: prism, cylinder, cone, sphere Volume formulas: Prism ( lwh ), Cylinder ( ), Cone ( ), Sphere ( ) Surface area includes all outer faces; for cylinders, remember both circular bases

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