A conical base covers an area of 30 cm2. Given a cone height of 6cm, determine its volume?
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Answer: D. 60 cm3
Explanation
The volume formula for a right circular cone equals one third of the base area times height. Multiplying the given base area of thirty square centimeters by the cone height of six centimeters. Dividing the product by three results in a final volume measurement of sixty cubic centimeters. Conical shapes taper uniformly from a flat circular or general base to a single top apex point. The one third factor distinguishes the volume of a cone from a cylinder with identical dimensions. Volume is expressed in cubic units of measurement for three dimensional spatial objects.
Manufacturing industries use cone volume formulas to design containers, funnels, and packaging. Geotechnical engineering calculates the volume of conical earth stockpiles using base area metrics. Architecture incorporates conical design elements while estimating necessary building materials. Option A suggests one hundred twenty cubic centimeters which multiplies the volume by two incorrectly. Option B proposes forty cubic centimeters which fails to match the proper formula calculation. Option C offers fifty cubic centimeters which results from an arithmetic computation error.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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