Question

Suppose a solid has as its base a circular region in the xy-plane. What method could be used to find the volume of the solid if every cross-section by a plane perpendicular to the x-axis is a triangle with one side in the base? Name the method only.

Answer #1

The base o a solid is the region in the xy plane bounded by y =
4x, y = 2x+8 and x = 0. Find the the volume of the solid if the
cross sections that are perpendicular to the x-axis are: (a)
Squares; (b) semicircles.

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.)

The base of a solid is the region in the first quadrant bounded
by the graph of y=cos x, and the x- and y-axes. For the solid, each
cross-section perpendicular to the x-axis is an equilateral
triangle. What is the volume of the solid?
A- 0.785
B-0.433
C -1.000
D- 0.340

Consider the region in the xy-plane bounded by the curves y =
3√x, x = 4 and y = 0.
(a) Draw this region in the plane.
(b) Set up the integral which computes the volume of the solid
obtained by rotating this region about
the x-axis using the cross-section method.
(c) Set up the integral which computes the volume of the solid
obtained by rotating this region about
the y-axis using the shell method.
(d) Set up the integral...

The base of a solid is the region enclosed by y=sin(x), y=0,
x=pi/4 and x=3pi/4. Every cross section is a square taken
perpendicular to the x-axis in this region. Find the volume of the
solid.

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.

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.

A
solid has a circular base of radius 1. Its parallel cross-sections
perpendicular to the base are parabolas. The largest parabola has
the equation y = 4 − x ^2 if placed on the plane. What is the
volume?
A. 9π/2
B. 1/2
C. π/2
D. 9/2
E. None of these

A. (1 point) Find the volume of the solid obtained by rotating
the region enclosed by ?= ?^(4?)+5, ?= 0, ?= 0, ?= 0.8
about the x-axis using the method of disks or washers. Volume =
___ ? ∫
B. (1 point) Find the volume of the solid obtained by rotating
the region enclosed by ?= 1/(?^4) , ?= 0, ?= 1, and ?= 6,
about the line ?= −5 using the method of disks or washers.
Volume = ___?...

The base of a solid is
the region bounded by y = 9 and y = x 2 .
The cross-sections of
the solid perpendicular to the x axis are rectangles of height 10.
The volume of the solid is

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