1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
coldgirl [10]
3 years ago
6

A solid is bounded below by the cone, z=x2+y2, and bounded above by the sphere of radius 2 centered at the origin. Find integral

s that compute its volume using Cartesian and cylindrical coordinates. For your answers use θ= theta.
Mathematics
1 answer:
ivolga24 [154]3 years ago
4 0

The cone z=\sqrt{x^2+y^2} and the sphere z=\sqrt{4-x^2-y^2} intersect in a circle of radius \sqrt 2 in the plane z=\sqrt2:

\sqrt{x^2+y^2}=\sqrt{4-x^2-y^2}\implies 2x^2+2y^2=4\implies x^2+y^2=2

\implies z=\sqrt{x^2+y^2}=\sqrt2

In Cartesian coordinates, the volume is then given by the integral

\displaystyle\int_{-\sqrt2}^{\sqrt2}\int_{-\sqrt{2-x^2}}^{\sqrt{2-x^2}}\int_{\sqrt{x^2+y^2}}^{\sqrt{4-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx

In cylindrical coordinates, the integral is

\displaystyle\int_0^{2\pi}\int_0^{\sqrt2}\int_r^{\sqrt{4-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta

You might be interested in
The median of the list of numbers is 16, 20, 36, 18, 22, 19, 22
Monica [59]
It's 20. Since it is median you will have to find the middle number. So in the sequence in order: 16, 18, 19, 20, 22, 22, 36. Next you will just find which number is in the middle. Also, tip: When doing this, if you have two medians such as 22 and 23. You will go to the number in between those, which would be 22.5.
5 0
3 years ago
Factor each expression 8 16 =
dalvyx [7]
Since they are just next to each other ill take it multiplication and that would be 128 if its not let me know and ill correct it 
8 0
4 years ago
Find the slope of the line passing through the points given below or state that the slope is undefined. Then indicate whether th
Sveta_85 [38]
Slope=(y2-y1)/(x2-x1)
=(5-4)/(4-2)
=1/2
slope > 0  => the line rises (from left to right).
7 0
3 years ago
At the same time of day, a man who is 75 inches tall casts a 50-inch shadow and his son casts a 22-inch shadow. What is the son'
nikitadnepr [17]

Answer: i think its 55 but im not sure

8 0
3 years ago
Read 2 more answers
Pablo and Mick are both waiters at a local Italian restaurant. They both are competing to see who gets more tips per week on ave
N76 [4]
Pablo has $594

Mick has $626

the difference is $32
5 0
4 years ago
Other questions:
  • Factorize a^2–b^2 Hence find the exact value of 2557^2-2547^2
    6·2 answers
  • you give a delivery driver $15.50 for a pizza that cost $12.50 you tell the driver to keep the change as a tip is the tip more t
    13·2 answers
  • Find the missing side length to the nearest tenth of a foot. hypotenuse is 14 and leg is 8
    10·1 answer
  • sylvia is carrying two bags of potatos, bag A and bag B. the weight of bag B is 3 pounds more than twice the weight of both bags
    13·2 answers
  • Solve for a and please provide a step by step easy explanation because I have to show my work.
    14·2 answers
  • Local winds are created by _____.
    15·2 answers
  • Solve 3(x - 2) < 18
    9·1 answer
  • Plz help. My brain is melted.
    11·1 answer
  • PLz help awarding brainlest to best answer
    14·2 answers
  • Can someone help me with this please :)))
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!