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Calculate the total, lateral, and base surface area of 3D shapes including cubes, spheres, cylinders, cones, and rectangular prisms.
Surface Area Formulas:
Cube: SA = 6s²
Sphere: SA = 4πr²
Cylinder: SA = 2πr(r+h)
Cone: SA = πr(r+l), l = slant = sqrt(r²+h²)
Rectangular Prism: SA = 2(lw + lh + wh)
Surface area is the total area of all outer faces of a 3D shape. It is measured in square units and is important for packaging, painting, and heat transfer calculations.
Lateral surface area refers to the area of only the sides (not the top and bottom bases). For a cylinder, it is the area of the curved side only.
Slant height is the distance along the lateral face of a cone, from the base edge to the apex. It is computed as sqrt(r² + h²) where r is radius and h is vertical height.
Surface area measures the outer covering of a shape (square units) while volume measures the interior space (cubic units). A cube with side 2 has SA = 24 and V = 8.
Surface area matters in real-world applications like calculating paint needed for walls, material for wrapping boxes, heat dissipation in electronics, and exchange rates in biology (like breathing and digestion).