Embedded Files
Welcome to the ACT math site for Ed-Co HS
Cube:
A cube is a three dimensional version of a square. To find the volume of a cube take the width times the height times the length. In the case of a cube you could just take the number to the third because all the sides should be the same length.
Volume = a3 (a times a times a (or a cubed))
Rectangular Prism:
A 3-D version of a rectangle.
Volume = LxWxH (length times width times height)
Triangular Prism:
A 3-D version of a triangle.
Volume = (1/3)bh (1/3 times base times height)
or even
Spheres:
A 3-D version of a circle.
Volume = (4/3)πr3 (4/3 times pi times r times r times r (or r cubed))
3-D Shapes & Volume
3-D Shapes & Volume
A three-dimensional (3-D) shape has three dimensions: length, width, and height. A 2-D shape has only length and width.
There are several 3-D shapes, several of which can be put in one of these categories: prism or pyramid.
Prism: a prism has two congruent shapes at opposite ends, parallel to each other, and connected by rectangular faces
Pyramid: a pyramid has a basic shape on the base, with triangular faces that come to a point
Depending on the shape at the ends/base of these two basic 3-D shapes, we can generate a whole bunch of prisms and pyramids.
Here are a few illustrations:
Note how the name is determined by the shape of the base: if the base is a square and the sides are triangles that come to a point, it is a square pyramid. If the two shapes at the ends are squares, parallel to each other and connected by rectangles, it is a square prism.
________________________________________________________________________________
There are two special 3-D shapes whose names don't include the word "prism" even though they technically are prisms:
1) Cube: a cube is essentially a prism (two squares opposite and parallel to each other, connected by rectangles), except that the connecting rectangles are actually squares. Cubes have six faces, all squares.
2) Cylinder: a cylinder is a prism because it has two circles opposite and parallel to each other, which are connected by a rectangle. It's not as obvious as other prisms, but think of a can of peas: if you take the label off, it is the shape of a rectangle.
________________________________________________________________________________
3-D shapes have volume: the amount of cubic space inside of them.
To find volume, you basically need the three dimensions: length, width, and height.
For prisms, the formulas are derived by taking the area of the shape at the end, and multiplying that times the figure's height.
Rectangular Prism: length x width x height
Cube: length x width x height OR side x side x side (since they are all the same)
Triangular Prism: (base x height ÷ 2) x height*
*this height is the height of the prism
Cylinder: (π x r x r) x height
For pyramids, the formulas are almost the same as for prisms, only they are divided by 3.
Square OR Rectangular Pyramid: (length x width x height) ÷ 3
Triangular Pyramid: ((base x height ÷ 2) x height*) ÷ 3
*this height is the height of the prism
Cone: (π x r x r x height) ÷ 3
________________________________________________________________________________
Volume examples!
Prisms:
1. Find the volume of this rectangular prism.
Recall the formula: length x width x height
(It won't change things if you're not sure which part is which, but usually length is the long side, width is the short side, and height is how tall it is.)
Plug in the numbers to the formula:
L x W x H = 12 x 4 x 6 = 288
To label volume, we use cubic units.
This rectangular prism has a volume of 288 cm3.
2. Find the volume of this cube.
Recall the formula: length x wideth x height OR side x side x side
Notice that only one side is labeled. This is okay since all the sides are the same. We know that length, width, and height are all 5 cm.
Plug the numbers into the formula:
L x W x H (or s x s x s) = 5 x 5 x 5 = 125
This cube has a volume of 125 cm3.
3. Find the volume of this triangular prism.
Recall the formula: (base x height ÷ 2) x height
First, let's identify each part.
The base is the "bottom" of one of the triangles: 7
The height is the height of one of the triangles: 5*
(If you get the 7 and 5 backwards, that's okay; just make sure you use numbers that are perpendicular to each other. Note that the other side of the triangle is not labeled. This side is not needed to find volume.)
The second height is the height of the prism: 6
Now plug in the numbers:
(base x height ÷ 2) x height = (7 x 5 ÷ 2) x 6 = 105
The volume of this triangular prism is 105 ft3.
For more formulas or further clarification, visit this site:
Page updated
Report abuse