Question

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.

Answer #1

Let us draw given region

Cross section perpendicular to the x axis are circles with diameter in xy plane

So height y is the diameter

Volume is given by the integral

Area of circle with diameter y is given by

But we have y=2sinx

X varies from 0 to π

So volume is

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.

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

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.

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 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

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.

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

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 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!

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

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