Volume And Surface Area Of Solids And Cylinders

                     Lesson 1

Volume                                                                                  Surface Area

Cylinder = πr²h                                           Cylinder(closed) = 2πr(r+h)

Cube   = l x b x h                                         Cylinder(open)   = 2πrh

Sphere   = 4/3πr³                                                      Cube = 2[(lb)+(bh)+(hl)]

                                                                        Sphere                      = 4πr²

Problem:                  The height of an open cylinder is 3 inches and the volume is 180 π cubic inches.

Find the surface area of this cylinder.

Step 1: Volume of a cylinder (V) = πr²h

Here, h = 3 in; V = 180π cu in;      180π=πr²h

Step 2: 180π = πxr²x3; r² = 180/3; r=7.7 in

Step 3:  Surface area of cylinder = 2πrh = 2x 3.14 x 7.7 x 6

= 290.1 sq in

 Step 4:                     The answer is:  290.1 sq. in

                                                            Try two practice problems:  

A.	The diameter of iron sphere is 6 cm. It is beaten and drawn into a wire of diameter 4 mm. Find the length of the wire.
B.	A cubical box has dimensions 10in × 6in × 4in. How many cubes dimension 3 in x 3 in x 3 in can be fixed in cubical box?

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