Question

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!

Answer #1

comment if you need further clarification!

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 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.

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

1. A volume is described as follows:
1. the base is the region bounded by y=2− 1/32 x^2 and y=0
2. every cross section parallel to the x-axis is a
triangle whose height and base are equal.
Find the volume of this object.
volume =
2. Find the volume of the solid obtained by rotating the region
bounded by
y=5x^2, x=1, and y=0, about the x-axis.
Need help with both please, thank you!

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

1) A volume is described as follows:
1. the base is the region bounded by y=2−2/25x^2 and y=0
2. every cross-section parallel to the x-axis is a
triangle whose height and base are equal.
Find the volume of this object.
volume =
2) The region bounded by f(x)=−4x^2+24x+108, x=0, and y=0 is
rotated about the y-axis. Find the volume of the solid of
revolution.
Find the exact value; write answer without decimals.

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 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

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.)

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