Calculus 12 Unit VII: Integration Worksheet – Solids of Revolution 1. Determine the volume of the shape generated when the area below the given equation is rotated about the x–axis, on the given interval for x. a) b) c) d) e) f) g) h) i) 2. Determine the volume of the shape generated when the area between the given curve and the y–axis is rotated about the y– axis, on the given interval for y. a) b) 3. Find the volume of the solid obtained when the given region is rotated about the x–axis. You should draw a sketch of the desired area to be rotated. a) The area bounded between and . b) The area bounded between , and . c) The area between and on the interval . 4. Find the volume of the sphere obtained when , , is rotated about the x–axis. 5. Find the volume of the ellipsoid obtained when , , is rotated about the x–axis. Solutions 1. a) b) c) d) e) f) g) h) i) 2. a) b) 3. a) b) c)
Worksheet Solids of Revolution1. Determine the volume of the
shape generated when the area below the given equation is rotated
about the xaxis, on the given interval for x.
a)
b)
c)
d)
e)
f)
g)
h)
i)
2. Determine the volume of the shape generated when the area
between the given curve and the yaxis is rotated about the yaxis,
on the given interval for y.a)
b)
3. Find the volume of the solid obtained when the given region
is rotated about the xaxis. You should draw a sketch of the desired
area to be rotated.a) The area bounded between and.b) The area
bounded between, and.
c) The area between and on the interval .
4. Find the volume of the sphere obtained when , , is rotated
about the xaxis.5. Find the volume of the ellipsoid obtained when ,
, is rotated about the xaxis.
