How to remember furmulas of 3d shapes like cube, sphere, cuboid, coin and cylinder
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Welcome to our guide on remembering three D shape formulas. Instead of just memorizing, we'll learn smart strategies that make these formulas stick. The key is understanding that volume measures the space inside a shape, while surface area measures the total area of all faces. When you see patterns between similar shapes, formulas become much easier to remember.
The first pattern to remember is that prisms and cylinders all follow the same rule: volume equals base area times height. For a cube, the base is a square with area s squared, and the height is s, giving us s cubed. For a cuboid, we multiply length times width times height. For a cylinder, the base is a circle with area pi r squared, multiplied by height h. Notice how they all follow the same base times height pattern.
The second important pattern is the one-third rule. Cones and pyramids always have exactly one-third the volume of cylinders and prisms with the same base area and height. This makes it easy to remember: if you know the cylinder formula pi r squared h, then the cone is simply one-third of that. The same relationship applies to any pyramid compared to its corresponding prism. For surface area, a cone has its circular base plus the curved side area.
The sphere is unique because it doesn't follow the base times height pattern. Instead, it has its own special formulas. The volume is four-thirds pi r cubed, and the surface area is four pi r squared. A great way to remember the surface area is that it equals exactly four times the area of a circle with the same radius. The key numbers to remember are 4 and 3. Notice how volume uses r cubed for three-dimensional space, while surface area uses r squared for two-dimensional area.
To summarize our formula memory strategies: First, remember that prisms and cylinders follow the base area times height pattern. Second, cones and pyramids always use one-third of their corresponding prism volume. Third, the sphere is unique with its four-thirds pi r cubed volume and four pi r squared surface area. Focus on understanding these patterns rather than memorizing individual formulas, and you'll find three D geometry much easier to master.