Surface area and volume review

Learning Objectives Calculate the surface area and volume of prisms, cylinders, pyramids, and cones. Calculate the surface area and volume of a sphere. Determine the surface area and volume of composite 3D figures by breaking them into simpler shapes. Solve for a missing dimension (e.g., radius, height, slant height) given the surface area or volume. Distinguish between lateral area and total surface area. Apply surface area and volume formulas to solve real-world problems. How much paint do you need to cover a water tower, and how much water can it hold? 💧 Let's review the geometry that answers these questions! This tutorial is a comprehensive review of calculating surface area (the 'wrapper') and volume (the 'filling') for common 3D shapes. Maste...

TermDefinitionExample Surface Area (SA)The total area of all the faces and curved surfaces of a three-dimensional object. It's the amount of material needed to cover the entire exterior.The amount of wrapping paper needed to cover a gift box. Lateral Area (LA)The surface area of a 3D object, excluding the area of its base(s).The paper label on a can of soup (it doesn't cover the top or bottom circles). Volume (V)The measure of the amount of space occupied by a three-dimensional object. It's the object's capacity.The amount of water that can fill a swimming pool. Slant Height (l)The distance measured along a lateral face from the apex (top point) to the base. It is used for pyramids and cones.On a cone, it's the distance from the tip down the side to the edge of th...

Prism and Cylinder Formulas Prism: SA = 2B + Ph, V = Bh | Cylinder: SA = 2\pi r^2 + 2\pi rh, V = \pi r^2 h Use for shapes with two parallel, congruent bases. 'B' is the area of the base, 'P' is the perimeter of the base, 'h' is the height, and 'r' is the radius. Pyramid and Cone Formulas Pyramid: SA = B + \frac{1}{2}Pl, V = \frac{1}{3}Bh | Cone: SA = \pi r^2 + \pi rl, V = \frac{1}{3}\pi r^2 h Use for shapes with one base that come to a point (apex). 'l' is the slant height, which is different from the perpendicular height 'h'. Sphere Formulas SA = 4\pi r^2, V = \frac{4}{3}\pi r^3 Use for perfectly round 3D objects. The only dimension needed is the radius 'r'.