If a solid spherical mass of 10 cm radius is reshaped into 8 identical solid spherical spheres, determine the surface area belonging to each sphere (in cm2)________?
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Answer: A. 100π
Explanation
The volume of a sphere scales with the cube of its radius, making the large sphere's volume proportional to 1000. Dividing this volume among eight identical smaller spheres gives each a proportional volume of 125, meaning its radius is 5 cm. Calculating the surface area of each small sphere using four times pi times the squared radius yields 100 pi square centimeters. The volume of a sphere is given by four-thirds times pi times the cube of its radius. The surface area of a sphere is calculated using the formula four times pi times the square of its radius. When a solid object is reshaped into multiple identical smaller objects, total volume remains perfectly conserved.
Option B underestimates the surface area by using an incorrect radius and formula application. Option C represents an intermediate calculation error that fails to match the spherical surface area formula. Option D calculates the surface area for a different radius size that does not satisfy the 8-sphere division.
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- Mathematics
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- Mathematics
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- —
- Difficulty
- medium
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