A sphere's surface area is 2464 cm2. If its radius is doubled, the surface area of_________?the new sphere will be
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Answer: C. 9856 cm2
Explanation
Doubling the radius of a sphere increases its total surface area by a factor of four. Multiplying the original surface area value by four gives the exact new surface area measurement. The resulting calculation yields ninety eight hundred fifty six square centimeters for the expanded sphere. The surface area of a sphere is proportional to the square of its radius length. When linear dimensions scale by a factor of two, surface areas scale by two squared. Geometric scaling principles allow rapid calculation of transformed shapes without recalculating full formulas.
Scaling principles are vital in physics and manufacturing when scaling up spherical storage tanks or vessels. Thermal radiation and heat dissipation rates depend directly on the total surface area of objects. Architects and designers use area scaling rules to estimate material requirements for proportional structures. Option a represents a slightly miscalculated value that fails the proper fourfold area scaling rule. Option b is incorrect because it does not follow the exact proportional square relationship for spheres. Option d incorrectly multiplies the original surface area by a factor of eight instead of four.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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