A rectangular prism has a length of 6 inches, a width of 8 inches and a height of 10 inches. Find the surface area and the volume. Then find another rectangular prism with the same area. What is the surface area.
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Expert's answer
2012-08-16T08:09:52-0400
Surface area S=2*6*8+2*6*10+2*8*10=96+120+160=376 square inches Volume V=6*8*10=480 cubed inches Another rectangular prism with the same area: given - the surface area of the new prism is 376 Let's try to find prism with square base, for example. Let side of the base be x and height of the prism y. So 2x^2+4xy=376 x^2+2xy=188 x(x+2y)=188=94*2 We can try? for example, x=2 Then x+2y=2+2y=94 2y=92 y=46 Let's verify: S=2*2^2+4*2*46= 376 , so that's it New prism has square base of side 2 inches& and height of 46 inches. Note, that it's only one of possible variants.
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