Math 6 Honors Periods 6 & 7 (Wednesday)

Volumes of Cylinders 10-7

A cylinder is a space figure that has two circular bases and one curved surface. The perpendicular distance between the bases is the height (h) of the cylinder.
If the base radius is r, then the base area, B is

πr²

Volume of cylinder = Base area X height
V = BH
V = πr² h
Find the volume of a cylinder having a base radius of 6 cm and a height of 8 cm.
B = πr² so B = π6²

36π

≈

36 X 3.14 113 ( rounded to three digits as our book requests)

V = Bh

113 X 8 = 904 904 cubic cm.

The volume of a cylinder or box is often called its capacity. For containers of liquids, capacity is usually measured in liters (L) or milliliters (mL)

Note: 1 L = 1000 cm³ and 1 mL = 1 cm³.


Note: Certain mathematics may have different meanings than they have in ordinary usage. For example, in everyday language, base refers to the bottom of an object and height refers to how tall an object is. In mathematical usage these terms have special meanings,

Math 6 Honors Periods 6 & 7 (Tuesday )

Polyhedrons 10-5

A polyhedron is a figure formed of polygonal parts of planes that enclose a region of space.

A prism is a polyhedron that has two congruent regions called bases that are parallel. Prisms are named according to their bases. Thus, a box is a rectangular prism. Take a look at Page 339 for some more examples of prisms.

A pyramid has only one base and a vertex. It is also named by the shape of its base. A triangular pyramid is also called a tetrahedron.
A regular polyhedron has all of its faces bounded by congruent regular polygons. There are only five such polyhedrons having 4, 6, 8, 12, and 20 faces.
Regular tetrahedron, cube, regular octahedron, regular dodecahedron, and regular icosahedron.

Check out Page 340 in our textbook for a picture of these.



Volumes Of Prisms 10-6

A polyhedron together with the region inside it is called a solid. The measure of the space occupied by a solid is called the colume ofthe solid.
Volume of prism = Base area X height
V = Bh where B = the Base area or the area of the base

Math 6 Honors Periods 6 & 7

Area of Circles 10-3

Recall that there are two formulas for the circumference C of a circle. If the diameter of the circle is denoted by d and the radius by r, then

C =πd and C = 2πr

Two approximations for the number π are 3.14 and

The part of the plane enclosed by a circle is called the area of the circle.

Formula

Area of circle = π · (radius)²

A = πr²

Find the area of the shaded regions. Use π ≈ 3.14

Recall that we give answers to only three digits when we use the approximation π≈ 3.14. In fact, sometimes to avoid approximation we give the answer in terms of π.

Find the area of the shaded region. Leave your answer in terms of π

(Look at your textbook for examples)

Area of shaded region = Area of large circle – Area of small circle.

We must first find the area of the small circle.

A = πr² = π2² = 4π

We then find the area of the large circle. Since the radius of the large circle is the same as the diameter of the small circle we know that the radius of the circle must be 4 m so A = πr² = π4²= 16π

Thus, the area of the shaded region is equal to 16π - 4π = 12π