Region R is bounded by the y-axis

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Region R is bounded by the y-axis, the curve

y=\sqrt{x}

, and the vertical line

x=1

in the first quadrant. Two solids share R as their common base. • Solid S has cross-sections perpendicular to the

x

-axis that are squares whose sides lie entirely within R. • Solid T has cross-sections perpendicular to the

x

-axis that are rectangles whose height is twice the length of their base (which lies in R). Which statement about the volumes of S and T is true? (a)

V_{T}>V_{S}

(b)

V_{S}>V_{T}

(c)

V_{S}=V_{T}

(d) The relationship between

V_{S}

and

V_{T}

cannot be determined without explicit integration.