Use Spherical Coordinate to Find the Volume Above the Cone $z ^ { 2 } = x ^ { 2 } + y ^ { 2 }$

question 68

Short Answer

Use spherical coordinate to find the volume above the cone $z ^ { 2 } = x ^ { 2 } + y ^ { 2 }$ and inside sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 2 a z$ .

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Definitions:

Half-life

The time required for half the atoms of a radioactive substance to decay into a stable form.

Cesium-137

A radioactive isotope of cesium with a half-life of about 30.17 years, commonly used in medical applications and industrial gauges.

Gamma Ray Emission

A type of radioactive decay where an unstable nucleus emits a gamma ray to become more stable.

Beta Particle Emission

A radioactive decay process where an unstable atomic nucleus emits a beta particle, which is a high-speed electron or positron, as part of the transformation to a stable state.