Solve the Problem $r$ Increases at the Rate Of $0.04$ Inches Per Second and That

question 307

Multiple Choice

Solve the problem.
-A high-altitude spherical weather balloon expands as it rises due to the drop in atmospheric pressure. Suppose that the radius $r$ increases at the rate of $0.04$ inches per second and that $r = 33$ inches at time $t = 0$ . Determine the equation that models the volume $\mathrm { V }$ of the balloon at time $t$ and find the volume when $t = 310$ seconds.

• A) \(\mathrm { V } ( \mathrm { t } ) = \frac { 4 \pi ( 0.04 \mathrm { t } ) ^ { 3 } } { 3 } ; 23,959.34 \mathrm { in } ^ { 3 }\)
• B) \(V ( t ) = \frac { 4 \pi ( 33 + 0.04 t ) ^ { 3 } } { 3 } ; 391,973.01 \mathrm { in } ^ { 3 }\)
• C) \(V ( t ) = 4 \pi ( 33 + 0.04 t ) ^ { 2 } ; 1,306,170.68\) in. 3
• D) \(V ( t ) = 4 \pi ( 0.04 t ) ^ { 2 } ; 1932.21\) in.3

---

Definitions:

Food Preservatives

Chemical substances added to food products to prevent spoilage and prolong shelf life by inhibiting microbial growth.

Suppressants

Agents or substances that inhibit the expression of certain actions, activities, or functions.

Angular Gyrus

A region of the brain in the parietal lobe that is involved in processing language, number processing, and spatial cognition, among other functions.

Cerebellum

A part of the brain located at the back of the skull, primarily involved in coordinating movement and balance.