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25 Sep 2006, 04:51
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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A cube and a right cylinder have the same surface area. If the height of the cylinder is as long as it is wide, then the volume of the cylinder is what percent higher than that of the cube?
(A) 6% (B) 13% (C) 29% (D) 33% (E) none of these
(A) 6% (B) 13% (C) 29% (D) 33% (E) none of these
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25 Sep 2006, 08:34
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I'm totally stuck on this one, but here's what I have so far:
Surface Area of the Cube:
(i) x = side of a cube
(ii) 6x^2 = surface area
Surface Area of the Cylinder
r = radius
h = height
(i) 2(pi)r^2 + 2(pi)rh = surface area
(ii) 2r = h since cylinder's width equals its height
(iii)((pi)h^2)/2 + (pi)h^2 = (3(pi)h^2)/2 = surface area
% difference between volume of cylinder and cube
(i) ((pi)r^2h - x^3)/x^3 = % difference
(ii) 2r = h
(iii) (((pi)h^3)/4 - x^3)/x^3 = % difference
(iv) 6x^2 = (3(pi)h^2)/2 => equivalence between SA of cube and cyl.
solving for the ratio between h and x:
(v) h^2/x^2 = 4/(pi) => h/x = 2/sqrt(pi) => h^3/x^3 = 8/(pi)^2
plugging everything into the % difference formula yields:
(vi) 8(pi)/4(pi)^2 - 1 = % difference
(vii) 2/(pi) - 1 = % difference
Formula (vii) yields a negative number...so would the answer be (E)?
Surface Area of the Cube:
(i) x = side of a cube
(ii) 6x^2 = surface area
Surface Area of the Cylinder
r = radius
h = height
(i) 2(pi)r^2 + 2(pi)rh = surface area
(ii) 2r = h since cylinder's width equals its height
(iii)((pi)h^2)/2 + (pi)h^2 = (3(pi)h^2)/2 = surface area
% difference between volume of cylinder and cube
(i) ((pi)r^2h - x^3)/x^3 = % difference
(ii) 2r = h
(iii) (((pi)h^3)/4 - x^3)/x^3 = % difference
(iv) 6x^2 = (3(pi)h^2)/2 => equivalence between SA of cube and cyl.
solving for the ratio between h and x:
(v) h^2/x^2 = 4/(pi) => h/x = 2/sqrt(pi) => h^3/x^3 = 8/(pi)^2
plugging everything into the % difference formula yields:
(vi) 8(pi)/4(pi)^2 - 1 = % difference
(vii) 2/(pi) - 1 = % difference
Formula (vii) yields a negative number...so would the answer be (E)?
25 Sep 2006, 09:51
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Just by looking at the numbers we know
1) obect is a Cube
2) object nearly is a cube! its highs is = its with
To me 2) means that it is the volume could only be marghinally lower than the cube = E
1) obect is a Cube
2) object nearly is a cube! its highs is = its with
To me 2) means that it is the volume could only be marghinally lower than the cube = E
