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Volume


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What is PRISM?
Two identical bases
Cubed (to the third power)
What units do we use with volume?
V = Bh
Volume of ANY prism
Capital B
Area of the base. Use the area formula of your shape!
Height
The shortest distance between the base of a geometric figure and its top.
volume of cylinder
area of circular base x height
Cavalieri's Principle
Same Base - Same Height - Volumes are the Same.
1/3 Bh
Volume of Pyramid
Slant Height
The height of each lateral face.
Apex
The Highest Point
V=1/3πr²h
Volume of Cone
Volume of sphere
V = 4/3πr^3
Volume of Hemisphere
(2/3) * πr³
cube
A solid shape that has: 6 square faces all equal in size, 8 vertices (corners), and 12 equal edges.
rectangular prism
a b c
b h
irregular prism
cylinder
A solid shape with one curved surface and two congruent circular bases.
pyramid
A solid shape with a polygon as a base and triangular faces that come to a point (vertex or apex)
cone
A solid shape with a circular base and a curved surface that come to a point (vertex).
sphere
A solid shape that is perfectly round like a ball. No faces, edges, or vertices.
ellipsoid
(4/3) pi r1 r2 r3
V=Bh
Prism: Volume
V=1/3Bh
Pyramid: Volume
volume
measures the amount of space taken up by the object.
prism
A solid geometric figure whose two end faces are similar, equal and parallel rectilinear figures, and whose sides are parallelograms.
(π)(r²)( h)
Volume of a Cylinder
b(h)
Volume of a Prism
(4/3π)(r³)
Volume of a Sphere
(1/3)(b)(h)
Volume of a Pyramid
(1/3)(π)(r²)(h)
Volume of a Cone