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| Math Central | Quandaries & Queries |
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Question from jhey, a student: The volume of a truncated prism is 6240 cu cm. The base is a right section in the form of an equilateral triangle. The edges perpendicular to the base are 15 cm, 18 cm, and 15 cm long. Find the length of one side of the base. |
Jhey,
The volume of a truncated triangular prim is
V = A(e1 + e2 + e3)/3
where A the area of a right section an e1, e2 e3 are the lengths of the lateral edges. [1]
You have V = 6240 cu cm, lateral edges of lengths 15, 15 and 18 cm and A is the area of an equilateral triangle. Let a be the length of a side of the equilateral triangle and write A in terms of a. Substitute the values into the equation for the volume of the truncated prism and solve for a.
Harley
[1] On the Volume of a Class of Truncated Prisms and Some Related Centroid Problems, by Murray S. Klamkin, Mathematics Magazine © 1968 Mathematical Association of America
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