# Math 117

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1.) 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.

A)(i) and (iv) B) (ii) and (iii) C(ii) D)(i) and (iii)

• Math 117 -

Cylinders and prisms have the same formula for the volume, namely:
Volume = base area * height
So this settles (i) or (ii)

The area of a square is L², and that of a circle of diameter is πD²/4 = 0.785D².
So if the square's side length is equal to the diameter of the base, then the area of the square is bigger than the circle. This should settle choices (iii) and (iv).

If you have doubts about your choice, post what you think for a check.