Question 204155: A rectangular solid and a circular cylinder have the same volume and the same height. The base of the rectangular solid is a square. Which (if any) of the following statements are true?
(i) The rectangular solid and the cylinder have the same base area.
(ii) The rectangular solid has a greater base area than the cylinder.
(iii) The side length of the square base of the rectangular solid is equal to the diameter of the cylinder.
(iv) The side length of the square base of the rectangular solid is less than the diameter of the cylinder.
Thank you so much for any help you can give me.
Found 2 solutions by RAY100, Alan3354:
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! The rectangular prism has Vol = Base area * Height
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Circular Cylinder has vol = Base Area * Height
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If height is same,,base areas are same therefore (i) ok
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(ii) the answer to (i) negates (ii)
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(iii) if base areas are same, A(r) =A(c),,,s^2 = pi* r^2
,,,,,,,therefore side of,,,square not equal radius,,,,negative
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(iv)if bases same, A(r) =A(c),,,s^2 = (pi* dia^2)/4,,,,
,,,,,,,,,therefore side < dia,,,TRUE
.
Have a great day
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! A rectangular solid and a circular cylinder have the same volume and the same height. The base of the rectangular solid is a square. Which (if any) of the following statements are true?
(i) The rectangular solid and the cylinder have the same base area.
(ii) The rectangular solid has a greater base area than the cylinder.
(iii) The side length of the square base of the rectangular solid is equal to the diameter of the cylinder.
(iv) The side length of the square base of the rectangular solid is less than the diameter of the cylinder.
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The volume of a solid that has a consistent cross-sectional area is that area times its height.
V = area*h
If the 2 volumes are equal, and the heights are the same, then the areas have to be equal.
That's (i).
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