AP® Calculus AB-BC

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Estimate Volume Using Trapezoid Riemann Sum


Deep Daryl wants to know how much water is in his lake. He knows that the average depth of his lake is 8 meters. The shape of his lake is a rugged oval and measures 80 meters in length, $L$. To estimate the area of the surface, Daryl took various width measurements in meters, $W$, to match with a given place along the 80 meter length. These measurements are as follows:

$L$ 0 30 40 50 80
$W$ 2 28 42 35 1

Using a Trapezoid Riemann Sum, estimate the volume of the water to the nearest whole cubic meter.


$1,725\text{ m}^3$


$2,130\text{ m}^3$


$13,800\text{ m}^3$


$17,040\text{ m}^3$