The ratio of diameters for two spheres is 1:2. What is the ratio of their surface areas?
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Answer: B. 1:4
Explanation
The ratio of the diameters of two spheres is directly equal to the ratio of their radii. Squaring the radius ratio of one to two determines the ratio of their respective surface areas. Multiplying one half by itself results in a final surface area ratio of one to four. The surface area of a sphere is proportional to the square of its radius multiplied by four pi. Linear dimension ratios remain identical whether expressed in terms of radii or diameters. Scaling principles dictate that surface areas increase quadratically relative to linear measurements.
Physics applications use spherical surface area ratios to study radiant heat transfer and light emission. Meteorology involves spherical geometry when analyzing droplet surface areas in cloud formation studies. Material science evaluates surface area to volume ratios of spherical particles in chemical reactions. Option A incorrectly assumes surface area scales linearly rather than quadratically with radius. Option C reverses the order of the ratio by comparing the larger sphere to the smaller one. Option D applies an incorrect cubic scaling factor typically reserved for volume calculations.
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- Mathematics
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- Mathematics
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