Surface area measures the total area of all surfaces of a three-dimensional object. Cylinders, cones, and spheres are common 3D shapes. Calculating th
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Why is the surface area of a sphere 4 times pi times r squared?
This formula comes from calculus and can be derived by integration. Intuitively, the surface area is 4 times the area of a great circle of the sphere, which is pi times r squared. The factor of 4 accounts for the three-dimensional curvature of the sphere.
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What is the difference between slant height and vertical height in a cone?
Vertical height is the straight-line distance from the apex perpendicular to the base. Slant height is the distance along the curved surface from the apex to the edge of the base. For surface area calculations, slant height is needed because it measures the actual distance across the lateral surface.
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How does the surface area change if you double the radius?
For a sphere, surface area is proportional to radius squared. Doubling the radius increases surface area by a factor of 4. For a cylinder or cone, doubling the radius increases surface area by more than a factor of 4 because both the base area and lateral area increase.
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