Question

2. Find the volume of the following solids with the given cross
section running along the frame F

given by the curves x = y^{2} - 4 and x = 5.

(A) Solid A has cross-sections perpendicular to the x-axis shaped
like squares with a side running

along F.

(B) Solid B has cross-sections parallel to the y-axis shaped
like semicircles with diameters running

along F.

(C) Solid C has cross-sections perpendicular to the y-axis shaped
like equilateral triangles with a

side running along F.

(D) Solid D has cross-sections parallel to the x-axis shaped
like isosceles right triangles with one

leg running along F.

Answer #1

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Find the volume of the following solids with the given cross
section running along the frame F given by the curves x = y^2 − 4
and x = 5..
(A) Solid A has cross-sections perpendicular to the x-axis
shaped like squares with a side running along F.
(B) Solid B has cross-sections parallel to the y-axis shaped
like semicircles with diameters running along F.
(C) Solid C has cross-sections perpendicular to the y-axis
shaped like equilateral triangles with a...

The region bounded by y=x^3, y=x, x=0 is the base of a solid. a)
If the cross sections are perpendicular to the
x-axis are right isosceles
triangles (congruent leg lies on the base), find
the volume of the solid. b) If the cross sections are perpendicular
to the y-axis are equilateral
triangles, find the volume of the solid.

Find the volume of the of the solid described as follows: The
base of the solid is the region enclosed by the line y=4-x, the
line y=x, and the y-axis. The cross sections of the region that are
perpendicular to the x-axis are isosceles triangles whose height is
equal to half their base. What is the volume of this solid (rounded
to two decimal places)? Please show work. Thanks much!

A solid region has a circular base of radius 3 whose
cross-sections perpendicular to the x-axis are equilateral
triangles.
Set up, but do not evaluate, an integral equal to the volume of
this solid region.Hint: the area of an equilateral triangle with
side length s is (s^2/4)(√3.)

2. Volume
(a) Compute volume of the solid whose base is a triangular
region with vertices (0,0), (1,0), and (0,1), and whose
cross-sections taken perpendicular to the y -axis are equilateral
triangles.
(b) Compute the volume of the solid formed by rotating the
region between the curves x=(y-3)^2 and x = 4 about the line y
=1

Find the volume V of the described solid
S.
The base of S is an elliptical region with boundary
curve 9x2 + 4y2 = 36.
Cross-sections perpendicular to the x-axis are isosceles
right triangles with hypotenuse in the base.

Find the volume of the solid ? if the base of ? is the
triangular region with
vertices (0,0), (3,0), and (0,2) and cross sections perpendicular
to y-axis are semicircles.
Please explain how you found x/3 + y/2 =1

1)Find the volume of the solid whose base is a circle with
equation x^2+y^2=36 and cross-sections are squares perpendicular to
the x-axis.
(a) Create the graph for this problem
(b) What is the volume of one 'slice'?
(c) What is the integral for the volume?
(d) What is the volume in exact form?
2) Find the volume of the region bounded by y=-x^2+4 and y=x+2
rotated about the line y=5
(a) Create the graph for this problem
(b) What is...

10. A spherical conductor of radius R = 1.5cm carries the charge of
45μ,
(a) What is the charge density (ρ) of the sphere?
(b) Calculate the electric field at a point r = 0.5cm from the
center of the sphere.
(c) What is the electric field on the surface of the sphere?
11. Two capacitors C1 and C2 are in series with a voltage V across
the series combination.
Show that the voltages V1 and V2 across C1 and...

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