SOLUTION: A block of lead has the shape of a rectangular solid whose dimensions are 1/2 in by 3/4 in by 1 in. This piece of oead is to be melted and recast into the form of a regular triang

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Question 1049357: A block of lead has the shape of a rectangular solid whose dimensions are 1/2 in by 3/4 in by 1 in. This piece of oead is to be melted and recast into the form of a regular triangular prism each basal edge of which is to be 1/2 in. What must be the altitude of this prism.
Answer by stanbon(75887) About Me  (Show Source):
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A block of lead has the shape of a rectangular solid whose dimensions are 1/2 in by 3/4 in by 1 in. This piece of oead is to be melted and recast into the form of a regular triangular prism each basal edge of which is to be 1/2 in. What must be the altitude of this prism.
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Volume of lead:: (1/2)(3/4)(1) = 3/8 in^3
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Volume of pyramid:: (1/3)LWH
L = W = 1/2
Solve for "H":
(3/8) = (1/3)(1/2)^2*H
3/8 = (1/3)(1/4)H
3/8 = (1/12)H
H = 12(3/8) = 9/2 = 4.5 in
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Cheers,
Stan H.
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