calc_tutorial_15_4_021

 
Problem Statement

{2,4,5,7,8}
pow(8,2)
pow(8,3)
round(2*512/3,3)

Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = 64, bounded above by the plane z = x and below by the xy-plane.

 
Step 1

Question Sequence

Question 1

Since one of the surfaces is a cylinder, it is best to use coordinates.

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 2

The region D in the xy-plane is precisely the semicircle x2 + y2 = 64 with x ≥ 0. Express D in polar coordinates.

0 ≤ r ≤

-π / 2 ≤ θ ≤

A.
B.
C.
D.

Express the lower and upper bounds in polar coordinates.

lower bound z =

upper bound z = x =

A.
B.
C.
D.

Correct.
Incorrect.

 
Step 3

Question Sequence

Question 3

Set up the triple integral for the volume in cylindrical coordinates.

Correct.
Incorrect.

 
Step 3

Question Sequence

Question 4

Evaluate the triple integral to find the volume of the given wedge-shaped region. Round your answer to three decimal places.

=

Correct.
Incorrect.