Question

Find the volume *V* of the described solid
*S*.

The base of *S* is an elliptical region with boundary
curve 9*x*^{2} + 4*y*^{2} = 36.
Cross-sections perpendicular to the *x*-axis are isosceles
right triangles with hypotenuse in the base.

Answer #1

Consider the solid S described below. The base of S is the
region enclosed by the parabola y = 1 - 9x^2 and the x-axis.
Cross-sections perpendicular to the x-axis are isosceles triangles
with height equal to the base. Find the volume V of this 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!

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.

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 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

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...

2. Find the volume of the following solids with the given cross
section running along the frame F
given by the curves x = y2 - 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...

Find the volume of the solid whose base is rotating around the
region in the first quadrant bounded by y = x^5 and y = 1.
A) and the y-axis around the x-axis?
B) and the y-axis around the y-axis?
C) and y-axis whose cross sections are perpendicular to x-axis
are squares

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.)

3) The base of a solid is the first quadrant region between the
curve y = 2 ⋅ sin xand the x-axis on the interval [ 0 , π ].
Cross sections perpendicular to the x-axis are semi circles with
diameters in the x-y plane. Sketch the solid. Find the volume of
the solid.

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