How many solid spheres of 6 cm diameter can be melted to form a solid metal cylinder 45 cm high and 4 cm in diameter?
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Answer: C. 5
Explanation
The volume of a sphere with a six centimeter diameter is calculated using the standard spherical volume formula. The volume of the cylinder is computed using its radius of two centimeters and height of forty five centimeters. Dividing the total volume of the cylinder by the volume of a single sphere yields exactly five spheres. Melting and recasting solid metal objects preserves the total volume of the material perfectly. Sphere volume is proportional to the cube of its radius multiplied by four thirds pi. Cylinder volume is calculated by multiplying pi by the squared radius and the height.
Metallurgical industries calculate volume ratios when melting down scrap metal to cast new components. Manufacturing processes rely on conservation of volume to determine material yield requirements. Geometry problems involving melting and recasting test spatial reasoning and volumetric formulas. Option A underestimates the number of spheres that can be formed from the cylinder volume. Option B is incorrect because the volumetric ratio simplifies precisely to the integer five. Option D overestimates the count by miscalculating the sphere or cylinder volume proportions.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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