An Object Is in the Shape Drawn Below; Its Boundary $y=2 x^{2}$

question 68

Multiple Choice

An object is in the shape drawn below; its boundary is obtained by rotating the parabola $y=2 x^{2}$ (for 0 $\le$ x $\le$ 1) around the y axis.(Units are in centimeters.) Suppose that the density of this object varies with height according to the rule $\rho$ (y) = 12 (2 - y) grams/cm³.Which of the following Riemann sums computes (approximately) the mass in grams of this object?

• A) \(\sum_{y=0}^{2} \pi \cdot y^{2} \cdot 12(2-y) \Delta y\)
• B) \(\sum_{y=0}^{2} \pi \cdot \frac{y^{2}}{4} \cdot 12(2-y) \Delta y\)
• C) \(\sum_{y=0}^{2} \pi \cdot \frac{y}{2} \cdot 12(2-y) \Delta y\)
• D) \(\sum_{y=0}^{2} \pi \cdot y \cdot 12(2-y) \Delta y\)

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