Calculate surface area for various 3D shapes
Step 1: Select the 3D Shape
Choose from cube, sphere, cylinder, or cone.
Why: Each shape has a unique formula; different shapes require different dimensions.
Step 2: Identify Required Dimensions
Cube: side. Sphere: radius. Cylinder & Cone: radius and height.
Why: Each shape is defined by specific parameters; missing any prevents area calculation.
Step 3: Verify All Values Are Positive
Ensure all measurements are > 0 (no negative or zero dimensions).
Why: Negative dimensions are physically impossible; calculations with them are meaningless.
Step 4: Apply Shape-Specific Formula
Cube: SA = 6s². Sphere: SA = 4πr². Cylinder: SA = 2πr(r + h). Cone: SA = πr(r + l) where l = slant height.
Why: Each formula accounts for the unique geometry of faces/surfaces in that shape.
Step 5: Verify Result in Context
Check that the surface area value is reasonable relative to the shape’s dimensions.
Why: Unexpected results may indicate input errors or formula misapplication.
Cube (s): SA = 6s²
Sphere (r): SA = 4πr²
Cylinder (r, h): SA = 2πr(r + h)
Cone (r, h): SA = πr(r + l) where l = √(r² + h²)
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