Question

A volume is described as follows:

1. the base is the region bounded by x=−y2+8y+50x=-y2+8y+50 and
x=y2−24y+146x=y2-24y+146;

2. every cross section perpendicular to the *y*-axis is a
semi-circle.

Find the volume of this object.

Answer #1

Question 1. A volume is described as follows:
1. the base is the region bounded by y=e^3.5x, y=3.5x^2+0.1 and
x=1;
2. every cross section perpendicular to the x-axis is a
square.
Find the volume of this object.
volume =
Question 2. Use cylindrical shells to find the volume of the
solid generated by rotating the curve y=4ln(x) about the x-axis for
1 ≤ x ≤ e.

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 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 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 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.

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 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

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.

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 V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
y = 5x4, y = 5x, x ≥
0; about the x-axis
Find the area of the region enclosed by the given curves.
y = 3 cos(πx), y = 12x2 −
3
Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
2x = y2, x = 0, y =
5; about the...

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