# Calculus

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/(4-x). 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.

1. 👍 0
2. 👎 0
3. 👁 125

## Similar Questions

1. ### art103

Describe the shapes in this painting. Are the shapes organic or geometric? Which ones? Describe how the shapes interact, or "touch" each other. Are the edges of the shapes soft or hard? Do they bump, blend, or overlap? Support

2. ### visual

"Street, Dresden", 1907, oil on canvas by Ernst Ludwig Kirchner. Describe the shapes in this painting. Are the shapes organic or geometric? Which ones? Describe how the shapes interact, or "touch" each other. Are the edges of the

asked by Maggie on September 15, 2012
3. ### visual

"Street, Dresden", 1907, oil on canvas by Ernst Ludwig Kirchner. Describe the shapes in this painting. Are the shapes organic or geometric? Which ones? Describe how the shapes interact, or "touch" each other. Are the edges of the

asked by Maggie on September 15, 2012
4. ### art 103

"Street, Dresden", 1907, oil on canvas by Ernst Ludwig Kirchner. Describe the shapes in this painting: Are the shapes organic or geometric? Which ones? Describe how the shapes interact, or "touch" each other. Are the edges of the

asked by kim on June 12, 2016
5. ### art 103

"Street, Dresden", 1907, oil on canvas by Ernst Ludwig Kirchner. 1.Describe the shapes in this painting: Are the shapes organic or geometric? 2.Which ones? Describe how the shapes interact, or "touch" each other. 3.Are the edges

asked by jene on June 8, 2015
6. ### art

The Visual Elements: "Street, Dresden", 1907, oil on canvas by Ernst Ludwig Kirchner Describe the shapes in this painting. Are the shapes organic or geometric? Which ones? Describe how the shapes interact, or "touch" each other.

asked by Olivia on September 14, 2012
7. ### algebra

why are these equations poor models of hitting a baseball: y= -0.002x(x-433.1) I get maximums of (216,93). Other problems' maximums are in the (220, 100)range. So are they poor models because the distance and heights are

asked by Anil on October 8, 2011
8. ### Elem. ED.

Art and math are being integrated when students: 1. draw more than 1 picture on a page. 2. use rectangular paint pots. 3. identify geometric shapes when composing a picture. 4. insist on using the same materials as their peers. Is

asked by Keisha on April 9, 2007
9. ### art

this image was created by using basic math concepts that include all of the following except A)knowing how to create a pattern B)using understanding the angles of the shapes C) a basic understanding of different geometric shapes.

asked by tom on October 5, 2016
10. ### Early Childhood Ed.

When a teacher shows children how to do a sponge painting with geometric shapes and then shows pictures of geometric shapes during group time,the teacher is probably using art to: A. create seat work B. discourage child-directed

asked by Keisha on April 8, 2007

More Similar Questions