Calculus
posted by Alex .
Hello. I'm having problems with a couple of Calculus questions that involve maximums of geometric shapes.
The first one is:
1. Find the dimensions and minimum volume of a right circular cone which can be circumscribed about a sphere of diameter 8.
What I have is used similar triangles.
The two ratios are y/4 = (y+4)/(x+4).
I ended up isolating for x and got x = [(4y+16)/4]  4.
Then I used this information to plug into the volume of a cone formula but I can't get it right so can someone tell me what I'd do next or tell me if I made a mistake? Any help is appreciated. Thanks.
2. A right square0based prism has to fit inside a cone that has a height of 9.0cm and a radius 4.0cm, so that the top four corners of the prism touch the cone. What are the dimensions of the prism of the maximum volume? What is the maximum volume?
Again, I used similar triangles for this questions.
My ratios are 9/4 = h/(4x). Then I isolated h and got h = 9  2.25x.
At this point, I plugged in h into the formula for the volume of a prism, this one being x^2h but I compared my answer with another persons and when they isolated h, they had h = 1.125 because their ratio was 9/4 = h/(1/2)x.
So I'm unsure what is correct.
Any help is much appreciated. Thanks a lot.
Respond to this Question
Similar Questions

Calculus 2
I am having so many problems with these volume problems, 1. Find the volume of a the solid obtained by rotating the region enclosed by: x = 2y and y^3 = x with y>0 about the x axis 2.Find the volume of cone of height h = 250 and … 
calculus
Find the dimensions of a right circular cone, that holds one liter and is made with a minimum amount of sheet metal. It is open on the top. 
calculus
A right triangle of hypotenuse L is rotated about one of its legs to generate a right circular cone find the largest volume that such a cone could occupy 
calculus
A right triangle of hypotenuse L is rotated about one of its legs to generate a right circular cone find the largest volume that such a cone could occupy 
Calculus
A right circular cone is inscribed in a sphere of radius r. Find the dimensions of the cone that maximize the volume of the cone. 
Calculus
A right circular cone is inscribed in a sphere of radius r. Find the dimensions of the cone that maximize the volume of the cone. 
calculus
A right triangle with hypotenuse 5 inches is revolved around one of its legs to generate a right circular cone. Find the radius and height of the greatest volume cone. 
Math  Calculus I
Optimization Problem: Find the dimensions of the right circular cylinder of greatest volume inscribed in a right circular cone of radius 10" and height 24" 
Maths
A right circular cone is circumscribed about a sphere of radius a .If h is the distance from the centre of the sphere to the vertex of the cone. Show that the volume of the cone is 1/3pi a^2(a+h)^2/(ha). Find the angle of a cone when … 
Calculus
Find the dimensions of the right circular cone of maximum volume having a slant height of 5 ft. See the figure.