
Volume Calculation Using Spherical Coordinates
Interactive Video
•
Mathematics, Science
•
11th Grade - University
•
Practice Problem
•
Hard
Mia Campbell
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the shape of the region E that we are trying to find the volume of?
A cube capped by a sphere
A pyramid capped by a sphere
A cone capped by a sphere
A cylinder capped by a sphere
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which coordinate system is used to set up the triple integral for finding the volume?
Spherical coordinates
Polar coordinates
Cylindrical coordinates
Cartesian coordinates
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the lower limit of integration for ρ in spherical coordinates?
π/2
7.25
0
2π
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the upper limit of integration for φ determined?
By using the equation of a cylinder
By forming a right triangle
By using the equation of the cone
By using the equation of the sphere
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the upper limit of integration for θ?
π
π/2
2π
0
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What substitution is used to evaluate the integral with respect to φ?
u = sin φ
u = tan φ
u = cos φ
u = φ
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of integrating with respect to ρ?
ρ^2 sin φ
1/3 ρ^3 sin φ
1/2 ρ^2 sin φ
ρ sin φ
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