what are the formula for volume of solid figures?

Question

all solid figures please... cone, sphere, pyramid, triangular prism, etc.

the more figures with correct formula, the better!

Answer 1

cone : Area of the base x height of the cone /3 = pi*r^2*h/3
r : The radius of the base circle
h: The height of the cone

sphere: 4/3*pi*r^3

pyramid: Area of the base of the pyramid x height /3
Volume of pyramid: A*h/3
A: The area of the base of the pyramid
h: The height of the pyramid
The base of the pyramid can have any shape: square, rectangle, triangle, hexagon etc...

Triangular prism: The area of the triangular prism x height of the triangular prism
Volume=A*h
A: area of the triangle
h: height of the prism
V: volume of the prism
Let's say we have a triangle with lengths a,b and c.
U=(a+b+c)/2
A=(U*(U-a)*(U-b)*(U-c))^0.5
V=(U*(U-a)*(U-b)*(U-c))^0.5*h

Answer 2

This is meant to be a volume, which is real. So perhaps the interval [0, 16] is for the y-axis, since the curve is only defined (real) for the purposes you want when x is on [0, 4], and the peak is over 16 (since the values at x = 2 and 3 are higher than that). This would also define the "bottom" of the solid as being the y=0 line, and the top of it the curve given. For any of these multivariable integrations, you need to consider what happens to a little volume element as you integrate. The volume of integration is a volume of a solid of revolution, so you have a radius which is your 'x' value, but the area has a height which varies from y = 0 to the lesser of the expression or 16. (There are 2 values of 'x' on the interval [0,4] where the expression is greater than 16.) [You could also do this by first integrating the entire volume of the solid of revolution--ignoring the limit on y--and then subtracting off the unwanted volume by looking at revolving the area which extends from y = 16 to the given expression, and from the 'x' crossover point to the second.] You still have to frame this in terms of it being a solid of revolution, but another answerer has talked about using the x value as the radius, etc., and a methodology for finding an answer. I just think that [0,16] must refer to the y values, because it you are looking for a real result. You should get a clarification.

Answer 3

http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeih/areaandvolumerev1.shtml- extracted from here!
Area of a parallelogram and trapezium
The area of a parallelogram is b × h


The area of a trapezium is 1/2 × h × (a + b)


Remember - h is the perpendicular height.
Volumes and surface areas
Prisms
A prism is a shape which has a uniform cross section.

The volume of a prism is the area of cross section x length.
The formula to remember is V = A × L


The volume of a cylinder is therefore r2 x length.


The surface area of a prism is the area of both ends, plus the sum of the areas of the sides.

The surface area of a cylinder is the area of both ends (2r2) plus the curved surface area (2rl)

Surface area of a cylinder:

= 2r2 + 2rl

= 2r(r + l)

Pyramids and cones
A pyramid is any shape that goes up to a point at the top. The base can be any shape, but when the base is a circle, it's called a cone.

The volume of a pyramid is: × base area × perpendicular height.


Therefore, the volume of a cone is: r2h.


The curved surface area of a cone is: rl (where l is the slant height).

Spheres


The volume of a sphere is: r3

The surface area of a sphere is: 4r2
Length, area and volume
How do we check that: r3 is the formula for a volume of a shape or that 2r(r + l) represents a surface area? We use dimensional analysis.

In both these formulae the letters r (radius) and l (slant height) represent lengths. The numbers (including , which is just 3.141....) are irrelevant, so we ignore them!

Here are the rules to remember for working out whether a formula is for a length, area or volume:

A formula with lengths occuring on their own is for a length.

A formula with lengths multiplied in pairs (eg r 2) is for an area.

A formula with lengths cubed (eg r3) will be for a volume.

Let's look at the formula for the volume of a sphere.

r3



If we remove all the numbers, the formula r3 becomes r3

r3 is length × length × length = volume

So r3 represents a volume.

Now let's look at 2r(r + l).

By removing all the numbers from 2r(r + l) we get r2 + rl

As r2 + rl includes a length squared, the formula represents an area. The formula is for the area of a cylinder.



Remember:

After all the numbers have been removed in a formula, you may be left with a combination of length, area and volumes. Here are the rules for simplifying these:


length length = length
area area = area
volume volume = volume

length × length = area

length × area = volume



volume/area = length

volume/length = area

Everything else is impossible (eg length + area, area × area).

Answer 4

Cylinder, triangular prism, square prism and anything else where the sides go straight up:

volume = base x height

Cone with any shape base, pyramid with any shaped base, any figure where lines go up from base to a single point:

volume = 1/3 x base x height

Sphere:

volume = 4/3 * Pi * radius cubed

Answer 5

Volume of the Cone = (1/3) pi r^2 h, pi = 3.142
Volume of the Sphere = (4/3) pi r^3, pi = 3.142
Volume of the Pyramid = (1/3) ( area of the base)* h, pi = 3.142
Volume of the Triangular Prism
= ( area of the trianglular base) h, pi = 3.142
Volume of the Cylinder= pi r^2 h, pi = 3.142
Volume of the Rectagular Parallelopiped
= length * breadth * height
Volume of the Cube = ( length)^3

Answer 6

Volume Formula for a sphere

V = 4/3 π r³

Volume formula for a clinder

V = π r² h

Volume formula for a cone

V = 1/3 π r² h

Volume formula for a Prism

V = B h

Volume formula a Pyramid

V = 1/3 B h

- - - - - - - - - -s-

Answer 7

For a cube it is Volume= Length x Width x Height

Answer 8

That's easily looked up on google

I'll give you the one I know from memory:

Sphere is (4/3)(pi)(r^3)

Answer 9

for a cube it is l*b*h