Question

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

Answer #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

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 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

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.)

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.

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

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.

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...

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