A Cylindrically-Shaped Mug with a 3cm Radius and a 10cm $\rho$

question 40

Multiple Choice

A cylindrically-shaped mug with a 3cm radius and a 10cm height is filled with tea.You have added some sugar to the tea, which tends to settle to the bottom of the mug.It turns out that the density $\rho$ of sugar (in gm/cm³) in the tea, as a function of the height, h, in cm, above the bottom of the mug, is given by the formula $\rho$ (h) = 0.025(10 - h) .Which of the following Riemann sums approximates the total mass of sugar (in grams) in the mug of tea?

• A) \(\sum_{\text {allslices }} 3 \pi(0.025)(10-h) \Delta h\)
• B) \(\sum_{\text {allslices }} 9 \pi(0.025)(10-h) \Delta h\)
• C) \(\sum_{\text {allslices }} 3 \pi(0.025)(10-h)^{2} \Delta h\)
• D) \(\sum_{\text {allslices }} 9 \pi(0.025)(10-h)^{2} \Delta h\)

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Definitions:

Nearest Whole Number

A round-off method where decimal values are rounded to the closest integer.

Net Operating Income

A financial metric that calculates a company's profit after subtracting operating expenses, excluding taxes and interest payments.

Traceable Fixed Expense

Fixed costs that can be directly associated with a specific product, department, or segment of a business, facilitating more accurate financial analysis.

Net Operating Income

The profit generated from a company's core business operations, excluding expenses and revenues not directly related to its main activities.