Solve the Problem $7 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$

question 256

Multiple Choice

Solve the problem. Round your answer, if appropriate.
-The volume of a sphere is increasing at a rate of $7 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$ . Find the rate of change of its surface area when its volume is $\frac { 4 \pi } { 3 } \mathrm {~cm} ^ { 3 }$ . (Do not round your answer.)

• A) \(14 \mathrm {~cm} ^ { 2 } / \mathrm { sec }\)
• B) \(\frac { 28 } { 3 } \mathrm {~cm} ^ { 2 } / \mathrm { sec }\)
• C) \(14 \pi \mathrm { cm } ^ { 2 } / \mathrm { sec }\)
• D) \(\frac { 1 } { 3 } \mathrm {~cm} ^ { 2 } / \mathrm { sec }\)

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Definitions:

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A minimally invasive procedure to open up blocked coronary arteries, allowing blood to circulate to the heart muscle.

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A condition characterized by the narrowing of the coronary arteries due to the buildup of plaque, leading to reduced blood flow to the heart.

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The volume of blood the heart pumps through the circulatory system in one minute.

LDL

Low-density lipoprotein, often referred to as "bad" cholesterol, which can build up in the walls of arteries leading to heart disease.