Find the Mass of a Solid Hemisphere of Radius 5 $\frac { 625 } { 4 }$

question 74

Multiple Choice

Find the mass of a solid hemisphere of radius 5 if the mass density at any point on the solid is directly proportional to its distance from the base of the solid.

• A) \(\frac { 625 } { 4 }\) k \( \pi\)
• B) \(25\) k \( \pi\)
• C) \(\frac { 25 } { 4 }\) k \( \pi\)
• D) \(\frac { 125 } { 4 }\) k \( \pi\)

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Definitions:

Allylic Carbons

Atoms of carbon that are positioned next to a carbon-carbon double bond in a molecule, often exhibiting unique reactivity due to their position.

Cholesterol

A waxy substance found in the lipids (fats) in the blood, essential for the creation of vitamin D, steroid hormones, and bile acids, but high levels can lead to health risks.

Highest Occupied

Refers to the Highest Occupied Molecular Orbital (HOMO), which is the top-most energy molecular orbital that is occupied by electrons in a molecule under the ground state.

π MO

Pi molecular orbitals are formed by the overlap of p orbitals that are oriented parallel to each other, playing a key role in the bonding of molecules with conjugated systems.