Question

use
cylindrical coordinates: A cylindrical hole of radius a is bored
through the center of a solid sphere of radius 2a. Find the volume
of the hole.

Answer #1

Use cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
z =
x2 + y2
and the sphere
x2 + y2 + z2 = 128.

1)
Use triple integration to find the volume of a sphere with
radius 5 in cylindrical, spherical, and cartesian coordinates.
Evaluate them all.

Use cylindrical coordinates to find the volume of the solid
bounded by the graphs of z = 68 − x^2 − y^2 and z = 4.

Use a triple integral in cylindrical coordinates to find the
volume of the sphere x^2+ y^2+z^2=a^2

Use spherical coordinates.
(a) Find the centroid of a solid homogeneous hemisphere of
radius 1. (Assume the upper hemisphere of a sphere centered at the
origin. Use the density function
ρ(x, y,
z) = K.
(x, y, z) =
(b) Find the moment of inertia of the solid in part (a) about a
diameter of its base.
Id =

Conical drill is used to drill a hole through the middle of a
sphere, that has a 10 cm radius. After the drilling there has
appeared a conical tunnel through the sphere, where one difference
has 6 cm diameter and the other difference has 8 cm diameter. Find
the volume of this punched sphere.

Use cylindrical coordinates to find the volume of the region
in the first octant bounded by a cylinder ?^2+ ?^2= 9 and a plane
2? + 3? + 4? = 12.

Use polar coordinates to find the volume of the given solid.
Inside the sphere x2 + y2 + z2
= 16 and outside the cylinder x2 + y2 = 4

Use cylindrical coordinates. Where E lies below the cone ϕ = π/4
and above the sphere ρ = 1. E is a region in the first octant.

A hole is drilled through the center of Earth. The gravitational
force exerted by Earth on an object of mass m as it goes
through the hole is
mg(r/R),where r is the
distance of the object from Earth's center and R is the
radius of Earth (6.4×106m).
A. Would this be a comfortable ride?
a)Going through the hole would be an uncomfortable ride because
of the extreme temperature in the interior of Earth.
b)Going through the hole would be...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 21 minutes ago

asked 26 minutes ago

asked 26 minutes ago

asked 34 minutes ago

asked 55 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago