A Balloon (In the Shape of a Sphere) Is Being $\left( \mathrm { V } { } ^ { \circ } \mathrm { r } \right) ( \mathrm { t } )$

question 202

Multiple Choice

A balloon (in the shape of a sphere) is being inflated. The radius is increasing at a rate of 4 cm per second. Find a function, r(t) , for the radius in terms of t . Find a function, V(r) , for the volume of the balloon in terms of r . Find $\left( \mathrm { V } { } ^ { \circ } \mathrm { r } \right) ( \mathrm { t } )$

• A) \(( \mathrm { V } \cdot \mathrm { r } ) ( \mathrm { t } ) = \frac { 320 \pi \mathrm { t } ^ { 2 } } { 3 }\)
• B) \(\left( V { } ^ { \circ } r \right) ( t ) = \frac { 112 \pi t ^ { 3 } } { 3 }\)
• C) \(( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 256 \pi t ^ { 3 } } { 3 }\)
• D) \(( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 1024 \pi \sqrt { \mathrm { t } } } { 3 }\)

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Definitions:

Dividend Yield

A financial ratio measuring the dividend income relative to the price of the stock, indicating how much a company pays out in dividends each year relative to its share price.

Coupon Yield

The annual interest rate paid on a bond's face value, indicating the amount of interest received by bondholders annually.

Common Stock

Equity ownership in a corporation, where shareholders have voting rights and potentially receive dividends.

Capital Gains Rate

The capital gains rate is the tax rate applied to profits from the sale of assets or investments, which can vary based on the asset's holding period and the taxpayer's income level.