is this right?? VOLUME!!?

Question

I been thinking if these volume formulas are correct.
volume of a cube and Rectangular prism: Length* Width* Height

volume of a pyramid general formula: area of the base* height* 1/3 as a fraction.
volume of a pyramid with a rectangular base: length of base* width of base* height (of the pyramid) * 1/3 as a fraction.

can u also explain as simplist as u can the volume of a sphere, cone, cylinder, and a triangular prism? thanks a lot guys! :)

Answer 1

The ones you have are correct

all x/y numbers are fractions (4/3, 1/3 etc)

Sphere = 4/3 x pi x (r^3)
where r is the radius of the sphere (same as a circle but in 3D - so distance to the middle from the outside)

Cylinder = pi x (r^2) x h
where r is the radius of the circular cross section of the cylinder, h is the height

Cone = 1/3 x pi x(r^2) x h
where r is the radius of the circle at the base of the cone, h is the height from base to tip (note - not the length of the edge, but measured from centre of the circle to the tip of the cone)

Triangular prism (any prism with a constant cross section along the height) = A x h
where A is the area of the triangle (or whatever cross section you have) and h is the height of the prism

Answer 2

Wow. I never doubted these formuls, mostly because my granpa explained it.

See what he did was give me a triangular (had to make it), spherical (ball), and cylindrical (can) prism.

He asked me to fill each of the ones above with water and take the measurements I would need for their equations.

He also gave me a rectangular "prism" (box).

I first filled the pyramid prism and took the measurement of length of base, width of base and the height.

I multiplied them, divided by 3 and got a numerical answer (i forget what). Then he asked me to fill the metal box with the water in the pyramid.

I did this and took the length of the box, the width and the height of the water.

I calculated for volume of rectangular prism and got the same answer as the pyramid!

I asked him why and he said that the water volume did not change when I poured it to the metal box so the volume of the water was the same no matter what vessel it inhabited.

Just to be safe I repeated the process with the can and the plastic ball.
Lo and behold, I got the same volume for all.

That pretty much assured me but this might assure you:
http://www.ifigure.com/math/geometry/geometry.htm
http://en.wikipedia.org/wiki/Algebraic_geometry
http://www.ajdesigner.com/phpgeometricformulas/sphere_volume_v.php

Or just talk to a person who knows these...

Answer 3

The formulae you quote are all correct.

The volume of a sphere is (4*pi*r^3) / 3 where r is the radius.

The volume of a cone is (pi*r^2*h) / 3 where r is the radius of the base, and h is the vertical height (as for your other pyramid formulae, this is one third the area of the base multiplied by the height).

The volume of a cylinder is pi*r^2*h where r is the radius.

The volume of a triangular prism is one third the area of the triangle multiplied by the length of the prism. The area of the triangle is half its base multiplied by its height.

Answer 4

Volume sphere = (4/3) pi r^3 where r is radius
Volume of cone = (1/3)pi r^2 h (r= radius of base, h = height)
Volume of cylinder = pi r^2h
Volumme of triangular prism = Bh where B = area of triangular base = .5 X altitude X base.

Answer 5

1- Sphere volume=(4/3) x PI x r^3

2- Cylinder volume=PI x r^2 x H

3- Cone volume= (PI x D^2 x H) / 12

4- Triangular prism volume=1/2*length*width*height

PI=3.14159, r=radius, H=height, D=diameter

Answer 6

all correct

total surface area of cone = π r l + π r²
V of cyclinder = π r²h
total surface area of cylinder = 2π r h + 2π r²
V of cone = 1/3 π r²h
V of sphere = 4/3 π r³
V of triangular prism=1/2*length*width*height.

Answer 7

They are derived from calculus. The outline can be defined using a curve, then the volume found by rotating that curve around an axis. These equations result in the volume formulas for regular solids.

Answer 8

quantity 2 is a much extra helpful action picture, whether the two are favorites of mine. EDIT: the individuals who did no longer like 2 via fact it became into "uninteresting" are morons. an excellent variety of the individuals who say that have the ideas of a small baby.

Answer 9

http://www.gomath.com/htdocs/ToGoSheet/Geometry/volume.html here you will get all the information you want.bye

Answer 10

-it's not volume it's value,..,