A tumor has the same shape as the solid formed by rotating the
curve y =...
A tumor has the same shape as the solid formed by rotating the
curve y = 4x – x 2
around the x axis. Given that x and y are measured in centimeters,
what is the
volume of the tumor?
Find the volume of the solid of revolution that is formed by
rotating the region bounded by the graphs of the equations given
around the indicated line or axis
1.- y=9-x^2, y=0, around the x axis
2.- y=√x-1, x=5, y=0, around the x=5
3.- y=1-x, x=0, y=0, around the y= -2
4.- y=x^2, x=0, y=3, around the y axis
1-Find the volume of the solid formed by rotating the region
enclosed by
y=e^1x+2, y=0, x=0, x=0.7
about the y-axis.
2-Use cylindrical shells to find the volume of the solid formed
by rotating the area between the graph of x=y^9/2 andx=0,0≤y≤1
about the x-axis.
Volume = ∫10f(y)dy∫01f(y)dy where, find the f(y) and the voume.
3- x=y^5/2 andx=0,0≤y≤1 about the line y = 2 to find the volume
and the f(y) by the cylindrical shells
Use the Disk/Washer Method to find the volume of the solid of
revolution formed by rotating the region about each of the given
axes.
14. Region bounded by: y=4 - x^2 and y=0.
(a) the x-axis (c) y= -1
(b)y=4 (d) x=2
AND
17. Region bounded by: y=1/ sqrt((x^2) +1), x= -1, x=1 and the
x-axis.
Rotate about:
(a) the x-axis (c) y= -1
(b) y=1
Find the volume of the solid obtained by rotating the region
bounded by y = x 3 , y = 1, x = 2 about the line y = −3.
Sketch the region, the solid, and a typical disk or washer
(cross section in xy-plane).
Show all the work and explain thoroughly.
1 Find the volume of the solid obtained by rotating the region
bounded by y=sin(5x^2), y=0, x=0, and x=√π/5 about the y-axis.
2 Find the volume of the solid obtained by rotating about the
y-axis the region in the first quadrant enclosed by x=5y and y^3=x
with y≥0
3 The base of a solid is the region in the xy-plane bounded by
the curves y=25−x2 and y=0. Cross-sections of the solid, taken
parallel to the y-axis, are triangles whose height...
A frictionless pulley has the shape of a uniform solid disk of
mass 6.00 kg and radius 12.0 cm . A 3.60 kg stone is attached to a
very light wire that is wrapped around the rim of the pulley(Figure
1), and the stone is released from rest. As it falls down, the wire
unwinds without stretching or slipping, causing the pulley to
rotate. How far must the stone fall so that the pulley has 7.50 J
of kinetic energy?