# volume

1. ### Rate of change in volume of sand in conical shape.

A conveyor is dispersing sands which forms into a conical pile whose height is approximately 4/3 of its base radius. Determine how fast the volume of the conical sand is changing when the radius of the base is 3 feet, if the rate of change of the radius is 3 inches per minute. Answer provided...
2. ### Regular Tetrahedron

How to find the volume of a regular tetrahedron using calculus? V = ∫ dV = ∫∫∫ dx dy dz This is what I did first I was thinking to take a cross-sectional equilateral triangle and integrate it from 0 to h, but I could not figure out how to do that. Instead I integrated each variable as...
3. ### Volume of Hexagonal Pyramid - Using Integration from (0-h)

The Question: By using Riemann’s sum, synthesise a mathematical model for finding the exact volume of any ‘tepee’ tent of side s and height h. Here's what I have so far However, I am currently unsure if I am heading in the right direction, and am stuck at what comes next. Any help would be...
4. ### Volume of a Cylinder

How to find the volume of a cylinder in the spherical coordinates?
5. ### Riemanns Sum Problem

The Question: What I have so far: I have also proven that the vertical cross-sections result in the same formulae for Volume: The Questions: State one assumption that must be made and its associated effect in relation to finding a formula for the lightweight ‘pop-up’ tent. If the safety...
6. ### Calculate volume of irregular triangular pyramid using differences between prisms

Here's a picture to better depict what I'm talking about: The red shape is the irregular triangular pyramid, the blue shape is the triangular prism. All vertices of the pyramid have different z-values (except the ones shared with the prism). I could of course calculate the volume of the...
7. ### Finding the area and volume of a region bounded by two curves

Hi all, I am a bit confused as to how to find the region R bounded by two graphs. The specific problem is: The region R shown is bounded by the graphs of y=2^-x and y=2cos(x). a) Find the area of R b) Determine the volume of the solid generated by revolving R about the line y=3 c) Determine...
8. ### Change in Internal Energy

A 1-mol sample of an ideal diatomic gas at pressure of 1 atm and temperature of 490 K undergoes a process in which its pressure increases linearly with temperature. The final temperature and pressure are 720 K and 1.6 atm. Determine (a) the change in internal energy, (b) the work done by the...
9. ### Volume of a Wine Glass

Design a wine glass that may have a flat base, solid stem and curved shape defined by the function y = Square root of x. The glass must hold 100mL. set the dimensions of the glass and confirm that it will hold 100ml. Use calculus to calculate the volume of the glass itself if it has to be...
10. ### Finding the volume of an ellipse watermelon

An ellipse watermelon has a major axis 28cm and minor axis 25cm. The equation of the ellipse is y = 12.5 - 12.5x/145 Find the volume using calculusJust wondering if anyone can help me out on this question! I'm not quite sure how to answer it as I keep getting an abnormally large number.Thanks!
11. ### Help finding volume generated by revolving 2/(x+1)(2-x) around y axis

Hi. I need to find exactly the volume generated when the area bounded by y= 2/((x+1)(2-x)), the x and y axis, and x = 1 is revolved around the y axis. The correct answer should be 4pi*ln(2)/3 units. Thanks!
12. ### How to determine Range of Allowable Values in a Torus with a fixed volume?

I'm working on a project for calculus where we have to determine the range of allowable values in a torus. The torus equation is y = Sqrt(r^2-(x-R)^2). The volume equation is v = 2 [Pi]^2 *r^2* R (Where the volume is fixed at (Pi^2)/2) The Surface area equation is sa = 4 [Pi]^2 r R...
13. ### Need help with Volume of 2 Curves about x = 4

My two equations are y=10ln(x) and y= -x^4 - x + 4. They are bounded below by the x axis. I need to find the volume of the shape obtained by revolving them around the line x=4. I'm not sure what method I should use to solve this, or how I would set it up. Could somebody please help me with this?
14. ### volume of this shape

Hi, I have a little big mathematical problem. I wish to find the volume of this shape below. The volume V seems to be (I'm not sure if the result is correct) this bounded integral. So I need some help to calculate this integral ! Thanks
15. ### volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2 )

By using spherical coordinates , find the volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2 ) , below by plane z = 0 ... Calculus III - Spherical Coordinates I'm having problem finding my Φ .... Here's my diagram ... The shaded part represent the volume...
16. ### volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

by using triple integral , find the volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9 . My ans is 36 , but the ans is 144... Is my ans wrong ?
17. ### volume bounded by different region

Well , i have 2 questions here : part a : I'm asked to find the volume bounded by plane y +z = 1 , y = (x^2) , xy plane and yz plane part b : I'm asked to find the volume bounded by plane y +z = 1 , y = (x^2) ,and z = 0 ... the ans given for part a is 4/15 , for part b is 8/15 However ...
18. ### volume bounded by the x+y+z =4

i'm asked to find the volume bounded by the x+y+z =4 . Why i cant use the formula of triple integral of x,y,z , where 0<x<4 , 0<y<4 and 0<z<4 ? if so , i ended up getting volume = 64 unit^3 , but the ans given is 32/3 . I gt 32/3 from ſſſ 4-x-y dx dy dz ....
19. ### Optimisation of volume question

A right circular cone is machined from a solid sphere of radius 30 cm. Find the ratio of thevolume of the cone to the volume of the sphere when the volume of the cone is a maximum Could anyone help me out with this question?
20. ### Functions problem - Volume halves every five minutes, what is the function?

The exact question is: "An ice cream cone is left sitting in the hot sun. Sarah notices that the ice cream melts and loses half of its volume every 5 minutes. If the starting volume was 125 mL, determine a function for the volume, with respect to the amount of time left out in the sun" So I...