Purchase Solution

Find the volume of the region common to the interiors of the cylinders x2+y2=a2 and x2^+z^2=a^2.

Not what you're looking for?

Ask Custom Question

Find the volume of the region common to the interiors of the cylinders x2+y2=a2 and x2^+z^2=a^2.

Attachments
Purchase this Solution
Solution Summary

The volume of the region common to the interiors of two cylinders is found. A cylinder function is provided.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

"/" is the integral sign.

Find the volume of the region common to the interiors of the cylinders x2+y2=a2 and x2+z2=a2.

Solution:

We know that volume V= z dx dy

V= sqrt( a^2-x^2) dx ...

Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Computing areas and volumes using multiple integrals.

    (2) Find the volume of the region in the first octant bounded by x + 2y + 3z = 6. (3) Find the area of the solid that is bounded by the cylinders x2+z2 = r2 and y2+z2 = r2.

  • Sample Question: Double Integral

    a2/2 +1+ a√(a2/ 4+1)] /4} This solution is comprised of a detailed explanation to set up an appropriate iterated integral to find the area of the region bounded by the graphs of y = x^3 - x and y = a(x^2) for x≥0.

  • Use Polar Coordinates to Find the Volume of a Ring-Shaped Solid

    36520 Use Polar Coordinates to Find the Volume of a Ring-Shaped Solid A cylindrical drill with radius 2 is used to bore a hole throught the center of a sphere of radius 7.

  • Integrals, moment of inertia, and Stokes theorem

    Find the volume over R and beneath the graph of f(x, y) = x + y. 4 Find the volume of the "ice cream cone" bounded by the sphere x2+y2+z2=1 and the cone z = ^/¯x2+y2-1 5 Find the moment of inertia around the z-axis of the solid bounded by

  • Multiple Integrals and vector calculus

    A) 9.6 B) 3.2 C) 8.0 D) No solution 8. A) B) 2 C) e -x sin(x) D) 9. Determine the volume of the solid bounded by the parabolic cylinders z = x2, z = 2x2, y = x2, and y = 8 - x2. A) B) C) D) 10.

  • Linear Homogeneous Partial Differential Equation

    (a) r = a2t (b) r - 3as + 2a2t = 0 where r = ∂2z/∂x2 , s = ∂2z/∂x∂y, t = ∂2z/∂y2 (c) (2D2 + 5DD′ + 2D′2)z = 0 (d) ∂3z/∂x3 - 3∂3z/∂x2∂y + 2∂3z/∂x∂y2 = 0 Solution :- (a) r =

  • Electric field and potential due to a charge distribution

    +a2) Ey = kqQ/a * (1/x - 1/Ö(x2+a2) Magnitude of the Electric field at point charge -q can be found by E = Ö (Ex 2 + Ey 2) E = kqQÖ2/a [1/x2 - 1/xÖ(x2+a2)]1/2 The direction of E also can be found using tan (theta) = Ey/Ex

  • Implicit differentiation

    Implicit Differentiation Find y" for x^2/a^2 - y^2/b^2 = 1 Solution: First, write y as a function of x, i.e. by multiply both sides of the equation by a^2*b^2 b2 x2 - a2 y2 = a2 b2 a2 y2 = b2 (x2 - a2 ) then we get y(x) y(

  • Simultaneous Equations for a System

    x2 + y2 = 1 y = |x| - a f Find all "a" which prevent the system to have no solutions From the second equation, |x| = y + a Squaring both sides, |x|2 = (y + a)2 = y2 + 2ay + a2 But |x|2 = x2, therefore, x2 = y2 + 2ay + a2 From the

View More Related Solutions