Solve the Problem $6 \mathrm {~cm}$ And Radius $\mathrm { r } \mathrm { cm }$

question 32

Multiple Choice

Solve the problem.
-The volume of a right cylindrical cone of height $6 \mathrm {~cm}$ and radius $\mathrm { r } \mathrm { cm }$ is $\mathrm { V } ( \mathrm { r } ) = 2 \pi \mathrm { r } ^ { 2 } \mathrm { cubic }$ centimeters (cm 3 ) . Find the instantaneous rate of change of the volume with respect to the radius $r$ when $r = 4 \mathrm {~cm}$ .

• A) \(16 \pi \mathrm { cm } ^ { 3 } / \mathrm { cm }\)
• B) \(16 \mathrm {~cm} ^ { 3 } / \mathrm { cm }\)
• C) \(4 \pi \mathrm { cm } ^ { 3 } / \mathrm { cm }\)
• D) \(32 \pi \mathrm { cm } ^ { 3 } / \mathrm { cm }\)

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Definitions:

Remainderman

A third party with the right to the remainder of the fee simple after the death of a life tenant.

Life Estate

A property interest where an individual (the life tenant) has the right to use, occupy, and benefit from a property during their lifetime, after which the property typically reverts to a remainderman.

Matrimonial Home

The dwelling that a married couple or civil partners occupy as their family home.

Will

A legal document that outlines how an individual's assets and properties will be distributed after their death.