A Spherical Balloon Is Inflated with Gas at the Rate $\frac { d r } { d t } = \frac { 3 } { 98 \pi } \mathrm { cm } / \mathrm { min }$

question 188

Multiple Choice

A spherical balloon is inflated with gas at the rate of cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is centimeters?

• A) \(\frac { d r } { d t } = \frac { 3 } { 98 \pi } \mathrm { cm } / \mathrm { min }\)
• B) \(\frac { d r } { d t } = \frac { 1 } { 98 \pi } \mathrm { cm } / \mathrm { min }\)
• C) \(\frac { d r } { d t } = \frac { 3 } { 196 \pi } \mathrm { cm } / \mathrm { min }\)
• D) \(\frac { d r } { d t } = 98 \pi \mathrm { cm } / \mathrm { min }\)
• E) \(\frac { d r } { d t } = 196 \pi \mathrm { cm } / \mathrm { min }\)

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Definitions:

Moral Treatment Movement

The Moral Treatment Movement was a 19th-century approach to mental illness emphasizing humane treatment, moral discipline, and the therapeutic benefits of nature and meaningful work.

Philippe Pinel

A French physician known for his humane treatment of psychiatric patients in the late 18th and early 19th centuries, often regarded as a founder of modern psychiatry.

Moral Treatment

An approach to mental health care in the 18th and 19th centuries that emphasized humane and respectful techniques.

Dorothea Dix

A pioneering advocate for the mentally ill in the 19th century, who played a key role in the creation of the first generation of American mental asylums.