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Q&A #4246 |
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Hi Margie, The two different formulas give you two different measurements. Lateral surface areas: the total number of unit squares on the side faces of the right prism. Volume: the total number of unit cubes which will fill the right prism. It is possible for the two formula to give you the same numeric answer; however, because they "talk" about different units they do not give you the same solution. If a right prism is 5 unit high and has a 2 unit by 3 unit rectangular base. Its lateral surface area is 5*(2 + 3 + 2 + 3) or 50 square units. (The height is a linear measurement and the perimeter is a linear measurement. linear units times linear units = square units) The volume of this prism is 5 * (2 * 3) or 25 cubic units. (The height is a linear measurement and the area is measured in squares. linear units times square units = cubic units) Here's a situation where the perimeter of a base and the area of a base are numerically the same: Height = 2 and base is a 4 x 4 square. Thus, the lateral surface area and the volume of the prism are NUMERICALLY the same. But remember, the formulas give you different units of measure, so the solutions ARE NOT the same. Hope this helps. -Jeanne, for the Teacher2Teacher service
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