Mathematics

Problem

Region R is bounded by the curve

y = \sqrt{x}

, the x-axis, and the vertical line

x = 4

. Cross-sections are taken perpendicular to the

y

-axis. • In Solid M these cross-sections are squares. • In Solid N the cross-sections are rectangles whose base equals that of the corresponding square, while the rectangle’s height equals the

y

-coordinate at that slice. Which of the following equals

\dfrac{\text{Volume of M}}{\text{Volume of N}}

? a)

\dfrac{15}{4}

\dfrac{64}{15}

\dfrac{256}{15}

1

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