A cone has a base of and a height of . The diameter is . What is the volume? If you were to dilate the cone with a scale factor of , what would the new radius be?

(I) V = 24π ≈ 75.3982 units³

(II) V = 192π ≈ 603.186 units³

General Formulas and Concepts:

Math - Symbols

π - pi, the number 3.1415926535897932384626433832795

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Geometry

DilationsDiameter: d = 2rVolume of a Cone:

Step-by-step explanation:

Step 1: Define

Height h = 8

Diameter d = 6

Base b = 5.4 (not needed in calculations)

Step 2: Find radius r

Substitute:                    6 = 2rIsolate r:                        3 = rRewrite:                         r = 3

Step 3: Find V of Normal Dimensions

Substitute:                    Exponents:                   Multiply:                        Evaluate:                      

Step 4: Find Dilations

Scale Factor: 2

Define radius:                    r = 3Dilate:                                 r' = 3(2)Multiply:                              r' = 6Define height:                    h = 8Dilate:                                 h' = 8(2)Multiply:                              h' = 16

Step 5: Find V of Dilated Dimensions

Substitute:                     Exponents:                    Multiply:                         Evaluate: