Solve the Problem $r$ And Volume $\mathrm { V } = \frac { 4 } { 3 } \pi \mathrm { r } ^ { 3 }$

question 436

Multiple Choice

Solve the problem.
-Suppose that the radius $r$ and volume $\mathrm { V } = \frac { 4 } { 3 } \pi \mathrm { r } ^ { 3 }$ of a sphere are differentiable functions of $\mathrm { t }$ . Write an equation that relates $\mathrm { dV } / \mathrm { dt }$ to $\mathrm { dr } / \mathrm { dt }$ .

• A) \(\frac { d V } { d t } = 4 \pi r ^ { 2 } \frac { d r } { d t }\)
• B) \(\frac { d V } { d t } = 4 \pi \frac { d r } { d t }\)
• C) \(\frac { d V } { d t } = \frac { 4 } { 3 } \pi r ^ { 2 } \frac { d r } { d t }\)
• D) \(\frac { d V } { d t } = 3 r ^ { 2 } \frac { d r } { d t }\)

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Definitions:

Operating Income

The profit realized from a business's normal operational activities, calculated before tax by subtracting operating expenses from gross profit.

Gross Profit

The financial performance metric that subtracts the cost of goods sold (COGS) from revenue, indicating how efficiently a company produces or sources its products.

Gross Margin

The difference between sales revenue and cost of goods sold, shown as a value or percentage, indicating the efficiency of sales relative to production costs.

Gross Sales

Gross sales represent the total sales revenue of a company without any deductions for returns, allowances, or discounts.