Question

**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.)

Answer #1

radius=3

so, we can get equation of circle

we can solve for y

now, we can find side of equilateral triangle

now, we can find area of triangle

now, we can set up integral for volume

now, we can solve each integrals

and combine them

**.............Answer**

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

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

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.

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.

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 base of certain solid is the triangle at (-4,2),(2,2), and
origin. cross-sections perpendicular to the y-axis are squares.
find the volume

The base of the solid S is the circle x2+y2=814. The cross
sections perpendicular to the base and the x-axis are semicircles.
Find the volume of S. Enter your answer in terms of π

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...

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

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