MGF 1106 – Section 9.4 Volume
Prisms: Two congruent bases, and the sides are rectangles
**Volume of a Prism = Bh where B = area of one base and
h = the distance between the two bases
Samples:
Rectangular Prism
Triangular Prism
Trapezoidal Prism Cylinder
(Circular Prism)
Hexagonal Prism
Trapezoidal Prism
Triangular Prism
PYRAMIDS – One base – "point" at the top – sides are triangles
1
**Volume of a Pyramid = Bh where B = area of the base and
3
h = perpendicular distance from the base to the point
Samples:
Rectangular Pyramid
Triangular Pyramid
Rectangular Pyramid
Right Triangular Pyramid
Cone (Circular Pyramid)
Cone (Circular Pyramid)
Spheres –
Volume =
4 3
r
3
Exercises:
Name the figure, select the formula, and calculate the volume.
1.
2.
3.
6 in
6cm
10 in
4.
14 ft
10 in
4cm
12 ft
8cm
5.
6.
7.
3 ft
2 ft
6 ft
20 ft
5 ft
5 ft
6 ft
10 ft
3 cm
8.
5 cm
9.
3 cm
12 ft
10. In baking a cake you have to choose between a round pan with 9 inch diameter and 7 X 9 in
rectangular pan. Both pans are 2 inches deep. Determine the volume of each pan.
11. A king-sized water bed mattress is 7 ft long, 7 ft wide, and 9 inches high. How many cubic feet
of water are needed to fill the mattress?
12. A hot water heater is in the shape of a circular cylinder. It has a height of 5 ft 6 inches and a
diameter of 18 inches. How many cubic feet of water will the tank hold?
13. Find the volume of the trapezoidal flower box shown below first in cubic inches then in cubic feet.
The box is 8 inches wide on the bottom, 12 inches wide on the top, 4 feet long, and 9 inches high.
More Examples:
Convert Cubic yards to cubic feet:
1 yd = 3 ft
So 1 yd 3 = 27 ft 3
To covert from yd 3 to ft 3 ---> multiply by 27
To covert from ft 3 to yd 3 ---> divide by 27
Polyhedron - closed surface formed by the union of polygonal regions
Face-
Edge-
Vertex-
Euler’s polyhedron formula-
Ex. A polyhedron has 4 verices and 4 faces. How many edges does it have?
Ex. A polyhedron has 12 vertices and 16 edges, how many faces does it have?