SOLUTION: Find the volume of a one-base paraboloid having on its base a circumference of 16π cm and an altitude of 10 cm.
Algebra.Com
Question 587934: Find the volume of a one-base paraboloid having on its base a circumference of 16π cm and an altitude of 10 cm.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I'm not sure my solution is what your calculus teacher expects, but hopefully it will help.
I like to visualize that paraboloid in x-y-z coordinates (in cm) as the space between
and (I'll find the right later).
The vertex of that paraboloid is at (0,0,0), with .
At we have the base of the paraboloid, which is a circle.
Its radius, R is such that -->
If we were allowed, I would search for volume, V, of a paraboloid with height h and base radius a, and find the formula
and for your paraboloid
In some calculus class, I would have some formula for volume of revolution solids, but I d not have it. (My 1973 Tom Apostol Calculus book has accumulated too much dust, and is probably too heavy and abstract to be of use).
So I figure out the radius, r, of a cross section as a function of z.
At , is -->
Now I have -->
Then, the area of a cross section circle is .
Now I'm ready to find the volume as
RELATED QUESTIONS
The base of a prism is a quadrilateral whose sides are 3.5 cm, 4 cm, 5 cm , and 6 cm. Its (answered by Edwin McCravy,ikleyn)
Find the volume of the spherical sector whose base has an altitude of 6 cm drawn on a... (answered by ikleyn)
the altitude of a triangle is 6 cm greater than its base. If its area is 108 cm^ find... (answered by josgarithmetic)
find the base of a triangle if its area is 766 sq. cm. and its altitude is 74... (answered by mananth,shreeaseem007@yahoo.in)
A hole 10 cm in diameter is to be punched out from a
right circular cone (base on top)... (answered by greenestamps)
The total surface area of a right cylinder is 84πcm² and the altitude is 11 cm. Find (answered by addingup)
The lateral surface of a right circular cylinder is 330π sq. cm.. If its altitude... (answered by macston)
find the area of a right triangle with hypotenuse 10 cm and base 16 cm... (answered by Alan3354)
The volume of a rectangular solid is 990 cubic cm and its total area is 675 sq. cm. If... (answered by josgarithmetic)