A sphere's lateral surface area equals 64 π cm2. Calculate its radius?
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Answer: C. 4 cm
Explanation
The surface area formula for any geometric sphere requires multiplying four by pi and radius squared. Equating four pi r squared to sixty-four pi simplifies algebraic cancellation of the constant pi. Solving for the radius squared yields sixteen which means the positive radius equals four centimeters. Spheres possess unique geometric properties where every surface point equidistant from the central point defines radius. The lateral surface area of a sphere equals its total surface area due to rotational symmetry. Extracting the principal square root of sixteen correctly provides the linear dimension in centimeters.
Manufacturing spherical pressure vessels requires accurate radius calculations to determine material thickness and structural strength. Astronomers compute planetary surface areas assuming near-spherical geometries when analyzing distant celestial bodies. Ballistics engineers use spherical surface area measurements to model aerodynamic drag coefficients on projectiles. Option A suggests one centimeter which produces a surface area far smaller than the given value. Option B proposes two centimeters which results in a surface area of sixteen pi square centimeters. Option D implies three centimeters which yields thirty-six pi square centimeters instead of sixty-four pi.
- Subject
- Mathematics
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- Mathematics
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- Difficulty
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