Using cylindrical coordinates, the volume of the solid in the first octant bounded by $x ^ { 2 } + y ^ { 2 } = 1$ and z = x is

A) $\frac { 7 } { 3 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 4 } { 3 }$
D) $\frac { 7 } { 2 }$
E) $\frac { 1 } { 2 }$

Question

Using cylindrical coordinates, the volume of the solid in the first octant bounded by $x ^ { 2 } + y ^ { 2 } = 1$ and z = x is

A) $\frac { 7 } { 3 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 4 } { 3 }$
D) $\frac { 7 } { 2 }$
E) $\frac { 1 } { 2 }$

Quizplus · Accepted Answer

The volume is calculated using cylindrical coordinates with limits for $ r $ from 0 to 1, $ \theta $ from 0 to $\frac{\pi}{2}$, and $ z $ from 0 to $ r \cos \theta $. The integral evaluates to $\frac{1}{3}$.

Using Cylindrical Coordinates, the Volume of the Solid in the First