Surface area of cylinders and cones

Learning Objectives Identify the components (radius, height, slant height) of cylinders and cones. Explain the concept of surface area as the total area of all faces of a 3D object. Apply the formula to calculate the surface area of a cylinder. Apply the formula to calculate the surface area of a cone. Use the Pythagorean theorem to find the slant height of a cone when given its radius and height. Solve real-world problems involving the surface area of cylinders and cones. Ever wondered how much paint you'd need to cover a giant water tank, or how much paper it takes to make a party hat? 🤔 It's all about surface area! In this lesson, you'll learn how to calculate the total area of the 'skin' of two common 3D shapes: cylinders and cones. Understandi...

TermDefinitionExample Surface AreaThe total area of all the surfaces (faces) of a three-dimensional object. Imagine 'unfolding' the object into a flat pattern (its net) and finding the area of that flat pattern.If you peel the label off a soup can and flatten it, then add the area of the top and bottom circles, you've found the surface area of the can. CylinderA three-dimensional geometric shape with two parallel circular bases of the same size connected by a curved surface.A can of soda, a battery, or a section of a pipe are all examples of cylinders. ConeA three-dimensional geometric shape that tapers smoothly from a flat circular base to a point called the apex or vertex.An ice cream cone, a party hat, or a traffic cone are common examples. Radius (r)The distance from th...

Surface Area of a Cylinder $SA_{cylinder} = 2\pi r^2 + 2\pi rh$ This formula calculates the total surface area of a cylinder. $2\pi r^2$ represents the area of the two circular bases (top and bottom), and $2\pi rh$ represents the area of the curved rectangular side (where $2\pi r$ is the circumference of the base and $h$ is the height). Surface Area of a Cone $SA_{cone} = \pi r^2 + \pi rl$ This formula calculates the total surface area of a cone. $\pi r^2$ represents the area of the circular base, and $\pi rl$ represents the area of the curved lateral surface (where $r$ is the radius and $l$ is the slant height). Pythagorean Theorem for Slant Height $l^2 = r^2 + h^2$ When the slant height ($l$) of a cone is not given, but the radius ($r$) and perpendicular height ($h...